Question

Find the value of p^2 + q^2 when p -q = 7 and pq = 9.​

Answer 1

P-q=7
Square both sides
p^2+q^2-2pq=49
So p^2+q^2= 49+ 18 =67

Answer 2

Answer:

the value of p² + q² = 67

Given problem:

Find the value of p² + q² when p - q = 7 and pq = 9.​

Step-by-step explanation:

from given data  p - q = 7  

do squaring on both sides

                     (p - q)² = 7²        

from  (a-b)² = a² + b² - 2ab  

                  p² + q² - 2pq = 49

                  p² + q² = 49 + 2pq

                  p² + q² = 49 + 2(9)      [ ∵ pq = 9 ]

                  p² + q² = 49 + 18 = 67

Answer 3

Given:

p-q=7

pq=9

To find:

$p^{2} +q^{2}$

Solution:

The required value of ($p^{2} +q^{2}$) is 67.

We will use the identity mentioned below to obtain the required value-

$(p-q)^{2}$=$p^{2} +q^{2}$-2pq

We are given that p-q=7 and pq=9.

We will substitute the values to obtain the required number.

Using the values,

$7^{2}$=$p^{2} +q^{2}$ -2(9)

49=$p^{2} +q^{2}$-18

49+18=$p^{2} +q^{2}$

67=$p^{2} +q^{2}$

Therefore, the value of ($p^{2} +q^{2}$) is 67.