# To state: Whether the equation ( p + q ) 2 = p 2 + q 2 is true or false. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

## To state: Whether the equation (p+q)2=p2+q2 is true or false.

Expert Solution

The equation (p+q)2=p2+q2 is false.

### Explanation of Solution

Suppose the values of p=2andq=1.

Substitute the value of p=2andq=1 in the L. H. S. of the equation (p+q)2=p2+q2,

L.H.S.=(2+1)2=32=9

Substitute the value of p=2andq=1 in the R. H. S. of the equation (p+q)2=p2+q2,

R.H.S.=22+12=4+1=5

Therefore, L.H.S.R.H.S.

In general, (p+q)2=p2+2pq+q2.

Thus, the equation (p+q)2=p2+q2 is false.

(b)

To determine

### To state: Whether the equation ab=ab is true or false.

Expert Solution

The equation ab=ab is true.

### Explanation of Solution

As long a and b are nonnegative real numbers.

Simplify the above expression ab=ab as follows,

L.H.S.=ab=(ab)12=a12b12=ab=R.H.S.

Suppose the values of a=9andb=4.

Substitute the value of a=9andb=4 in the L. H. S. of the equation ab=ab,

L.H.S.=9×4=36=6

Substitute the value of a=9andb=4 in the R. H. S. of the equation ab=ab,

R.H.S.=9×4=3×2=6

Therefore, L.H.S.=R.H.S.

As long a and b are nonnegative real numbers.

Thus, the equation ab=ab is true.

(c)

To determine

### To state: Whether the equation a2+b2=a+b is true or false.

Expert Solution

The equation a2+b2=a+b is false.

### Explanation of Solution

Suppose the values of a=2andb=1.

Substitute the value of a=2andb=1 in the L. H. S. of the equation a2+b2=a+b,

L.H.S.=22+12=4+1=5

Substitute the value of a=2andb=1 in the R. H. S. of the equation a2+b2=a+b,

R.H.S.=2+1=3

Therefore, L.H.S.R.H.S.

Thus, the equation a2+b2=a+b is false.

(d)

To determine

### To state: Whether the equation 1+TCC=1+T is true or false.

Expert Solution

The equation 1+TCC=1+T is false.

### Explanation of Solution

Suppose the values of T=3andC=2.

Substitute the value of T=3andC=2 in the L. H. S. of the equation 1+TCC=1+T,

L.H.S.=1+3×22=1+62=72=3.5

Substitute the value of T=3andC=2 in the R. H. S. of the equation 1+TCC=1+T,

R.H.S.=1+3=4

Therefore, L.H.S.R.H.S.

Thus, the equation 1+TCC=1+T is false.

(e)

To determine

### To state: Whether the equation 1x−y=1x−1y is true or false.

Expert Solution

The equation 1xy=1x1y is false.

### Explanation of Solution

Suppose the values of x=3andy=2.

Substitute the value of x=3andy=2 in the L. H. S. of the equation 1xy=1x1y,

L.H.S.=132=11=1

Substitute the value of x=3andy=2 in the R. H. S. of the equation 1xy=1x1y,

R.H.S.=1312=236=16

Therefore, L.H.S.R.H.S.

Thus, the equation 1xy=1x1y is false.

(f)

To determine

### To state: Whether the equation 1xax−bx=1a−b is true or false.

Expert Solution

The equation 1xaxbx=1ab is true.

### Explanation of Solution

As long a and b are nonnegative real numbers.

Simplify the above expression 1xaxbx=1ab as follows,

L.H.S.=1xaxbx=1xabx=1x×xab=1ab=R.H.S.

Thus, the equation 1xaxbx=1ab is true.

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