# lengthwhose areas are equal to their perimeters. [Hint: Theequations x2ythat (x 4)(y-4) 8.]3. For n 3 a given integer, find a Pythagorean triplehaving n as one of its members. [Hint: For n an oddinteger, consider the triple= z and x + y +z xy imply11(n21)2(n 1)п,20129 16Efor n even, consider the triple toomJons ol al10R(DOLB S (n, (n2/4) - 1, (n2/4) + 1).]do8 Dilenálozs pb03oorlw4. Verify that (3, 4, 5) is the only Pythagorean tripleinvolving consecutive positive integers. [Hint:Consider the Pythagorean triple (x, x + 1, x +2) andshow that x =3.]mo5.(a) Establish that there are infinitely manyPythagorean triples (x, y, z) in which x and y areconsecutive integers. [Hint: If (x, x + 1, z)happens to be a Pythagorean triple, so is(3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).](b) Find five Pythagorean triples of the form(x, x1, z).

Question
1 views help_outlineImage Transcriptioncloselength whose areas are equal to their perimeters. [Hint: The equations x2y that (x 4)(y-4) 8.] 3. For n 3 a given integer, find a Pythagorean triple having n as one of its members. [Hint: For n an odd integer, consider the triple = z and x + y +z xy imply 1 1 (n21) 2 (n 1) п, 2 0129 16E for n even, consider the triple toom Jons ol al 10R (D OLB S (n, (n2/4) - 1, (n2/4) + 1).] do8 Dilenál ozs pb 03 oorlw 4. Verify that (3, 4, 5) is the only Pythagorean triple involving consecutive positive integers. [Hint: Consider the Pythagorean triple (x, x + 1, x +2) and show that x = 3.] mo 5. (a) Establish that there are infinitely many Pythagorean triples (x, y, z) in which x and y are consecutive integers. [Hint: If (x, x + 1, z) happens to be a Pythagorean triple, so is (3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).] (b) Find five Pythagorean triples of the form (x, x1, z). fullscreen
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Step 1

Let three consecutive positive integers be x, x + 1, x + 2.

Note that, a Pythagorean triplet is a set...

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