Question

If p+q = 25 and pq = 200 then find p^2+q^2

Answer 1

Answer:

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Answer 2

Solution-:

$\displaystyle \large{ \sf{ \orange{given}}}$

p + q = 25

pq = 200

to find -:

p² + q²

Using -:

( p + q )² = p² + q² + 2pq

Let's begin

$\displaystyle \large{ \sf{(p + q) {}^{2} = p {}^{2} + q {}^{2} + 2pq}}$

Putting given value

$\displaystyle \large{ \sf{(25) {}^{2} = {p}^{2} + q {}^{2} + 2 \times (200)}}$

Now,,

$\displaystyle \large{ \sf{625 = p {}^{2} + q {}^{2} + 400}}$

transposing 400 on LHS

$\displaystyle \large{ \sf{625 - 400 = p {}^{2} + {q}^{2} }}$

now,,

$\displaystyle \large{ \sf{225 = p {}^{2} + {q}^{2} }}$

hence,,

$\displaystyle \large{ \sf{ \green{value \: of \: p {}^{2} + {q}^{2} = 225 \: \: ans}}}$