Question

1. Find the value of:
p^2 + q^2 if p-q=6 and p + q = 14​

Answer 1

Step-by-step explanation:

p-q=6

p+q=14

p-q+p+q=6+14

2p=20

p=10

=>q=14-p

q=14-10

q=4

p^2+q^2=10^2+4^2

=>100+16

=>116

Answer 2

Given:

The value of p - q and p + q is 6 and 14 respectively.

To Find:

The value of p² + q².

Solution:

1. The given equations are,

• p - q = 6 ( Assume as equation 1 )
• p + q = 14 ( Assume as eqaution 2 )

2. Consider equation 1,

=> p - q = 6,

=> Apply square on both the sides,

=> p² + q² - 2pq = 36. ( Assume as equation 3 ).

3. Consider equation 2,

=> p + q = 14​,

=> Apply square on both the sides,

=> p² + q² + 2pq = 196. ( Assume as equation 4 ).

4. Add equations 3 and 4,

=> p² + q² - 2pq + p² + q² - 2pq = 36 + 196,

=> 2p² + 2q² = 36 + 196,

=> 2(p² + q²) = 232,

=> (p² + q²) = 116.

Therefore, the value of (p² + q²) is 116.