Question

find the value of p^2+q^2 if pq=2 and p+q= 3

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Answer 1

ANSWER:

The values of $p^{2} +q^{2}$ is 5.

Step-by-step explanation:

Given that:

• $pq=2$

• $p+q=3$

     

To Find:

• the value of $p^{2} +q^{2}$  

Doing squares on both the sides :

 → $(p +q)^{2} =3^2$

Now, we use the property

$(a+b)^2=a^2+b^2+2 X a X b$

Put the values as :

• a = p

• b = q

Now, In equation,

• $p^2 +q^{2} + 2 X p X q =9$  

• $p^2 +q^2 +$ $2pq =9$

We know that :

• $pq=2$

So,  

• $p^2 +q^2 + 2 X 2 =9$

• $p^2 +q^2 + 4 =9$

Taking 4 from L.H.S. to R.H.S

• $p^2 +q^2 =9 - 4$

• $p^2 +q^2 =5$

The values of $p^{2} +q^{2}$ is 5.