if a and b are positive real number, then 0<(ab)1/2<=(a+b)/2.

Q: If a, b, c are integer powers of 2, prove that equation a³ + 64 = c does not have solution,…

A: Step:-1 Statement:-  Given Statement is  a3 +b4 =c5 ----(1) Counter Example:-  Take a=28,  b=26  and…

Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

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Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

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Q: Calculate the real values of x and y such that (x+y)³ is bigger than 8

A: Given: - The expression (x+y)3 is bigger than 8. To calculate: - The real values of x and y.

Q: O solve over all real numbers. 6. cotxsin2x = 5cotx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: How many positive integer solutions are there to x1 + x2 + x3 + x4 < 50 ?

A: We want to find the number of tuples x1, x2, x3, x4 that satisfy the given inequality. Note that for…

Q: Find all real solutions 4x^2+20x-11=0

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Q: Suppose X ÷ ( – 2) is 7x? – 2x – 6 with remainder 5. - - Then X %3D

A:

Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

A: Given a+b=120 .....1

Q: For each positive integer n, find the number of positive integers that are less than 210n which are…

A: ANSWER :

Q: If-2 is one root of x² +kx− 6 = 0, find the other root and the value

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Q: If x, y and z are real numbers and x*y°z0 > 0, which of the following must be positive?

A: Given  x8y9z10&gt;0

Q: Find all real solutions of the equation. 4(x + 1)1/2 - 5(x + 1)3/2 + (x + 1)5/2 = 0

A: 4x+112-5x+132+x+152=0

Q: Find the values between which the expression x2-4x+3/x2+3  lies where x is and an element of real…

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Q: Solve. (4и— 3) (9+ и) %— 0 (If there is more than one solution, separate them with commas.) ?

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Q: = (; ). -3 Find the general solutions of X' = AX with A = 1 -2

A: Consider the provided question,

Q: If -2 is a root of the equation x² + px - 6 = 0 and the equation x²- px + q = 0 and the equation x²-…

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: 2^{4x-4}=5^{5x-6}, solve for x and please show work.

A: Given; 24x-4=55x-6   ....1   As we know from the logarithmic rule; logaxb=b·logax, where x,a&gt;0…

Q: A positive integer is 4 less than another. If 6 times the reciprocal of the smaller integer is…

A: Let the smaller integer is 'x' and larger integer is 'y'.A positive integer is 4 less than…

Q: show that the equation 3x+2cosx+5=0 has exaclty one real root.

A: f(x)=3x+ 2 cos x +5

Q: The product two odd integers is even, whereas the product of an odd integer and an even integer is…

A: The product of two odd integers is odd. The product of an odd integer and an even integer is even.

Q: Find x so that x,x+2 and (x+3) are threee consecutive terms of GP

A: When a, b, c are in gp then b^2=ac.

Q: 4. Show that the real number VV2 – 2 is algebraic. (Here 2 is a real number that satisfies (2)3 =…

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5=0

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Q: Suppose that x, y and z are three positive numbers whose sum is 100 If P denotes the product of the…

A: Given,           Suppose that x,y and z are three positive numbers whose sum is 100.           Also,…

Q: Solve for all values of x: 6 + 1 9 - x X 9 - x

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Q: The product of any integer and 2 is greater than 2.

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Q: How many solutions are there to the equation: x1 + x2 + x3 = 19 where 1. x1, x2, x3 are all…

A: As per Bartleby guideline for more than one question asked only first is to be answered please…

Q: Given 0 ≤ 0 < 2π, solve 2tan0 - 6 = 0

A: Given query is to find the value of the theta.

Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: If x > y and a are a negative real number, this always applies

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Q: If [x] and [x] denote the fractional and integral parts of a real number x, respectively, solve {x +…

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Q: find a real root of equations following: 1- x³+x-5=0 2- x³+x-1=0, X°=1 3- x³+4x-2=0, ɛ =0.0001

A: To find- Real roots of the equation.

Q: Three consecutive odd integers are such that the sum of 5 times the first integer and 8 times the…

A: Three consecutive odd integers are given such that, The sum of 5 times the first integer and 8 times…

Q: Solve the inequality for real x:  3x – 7 &gt; 5x – 1

A: Given inequality:

Q: How many nonnegative solutions are there to the equation x1 + x2 + x3 + X4 + x5 = 21.

A: We need to find the number of nonnegative solutions of the equation  x1+x2+x3+x4+x5=21 Here, n=21…

Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

A: From the given information we want to find How many positive integer solutions are there to x1 + x2…

Q: Find a real root of 3*exp(-x/2)+4*In(x)-2 = 0 using False Position method with a=0.5 and b=2.0…

A: Given:            3*exp(-x/2)+4*ln(x)-2=0           3·e-x2+4lnx-2=0     By using False position…

Q: How many solutions are there to the equation x₁ + x₂ + x3 = 22, if each x, is a positive integer?…

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Q: 2tan(3x) + 3 = 1

A: subtract both sides by 3 divide both sides by 2

Q: Find a real root of 4*exp(-x/2)-3*In(x)-3 = 0 using False Position method with a=0.1 and b=2.0…

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Q: How can I show that there exists at least one solution in the set of real numbers for x5-x3+3x=5…

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Q: ues of p will 3x(4x+3)=-p have non-real root

A: Given Equation 3x4x+3=-p The value of p is found such that the equation has a non-real root.

Q: How many solutions are there to the equation x1 + x2 + x3 + x4 = 17 where all the x are nonnegative…

A: C320=1140

Q: If 1 is one root of the equation kx⁴ + (2k + 5)x³ + (3 – k) = 0, then the value of k is   A. 1 B. -4…

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Q: A(n) ______ number is a real number that cannot be expressed as a ratio of two integers

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Q: What is/are the value/s of k if the sum of the roots of x2 + kx + 3x = 1 is 3?

A: We know that if α and β be roots of a quadratic equationax2+bx+c=0, then α+β=-ba and αβ=caHere, the…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.