Question

]If p +q =13 and pq = 22, then find value of p2 + q2
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Answer 1

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$If p +q =13 and pq = 22, then find value of p2 + q2

$\bold{Given}$

$⟹\bold</p><p>{p + q = 13......(i)}$

$⟹</p><p>\bold{pq = 22}$

$⟹</p><p>\bold{p = \frac{22}{q} ......(ii)}$

$\bold{\red{Put\: value\: of\: p \:in \:equation (i)}}$

$⟹</p><p>\bold{p + q = 13}$

$\bold{ \frac{22}{q} + q = 13}$

$⟹</p><p>\bold{22 + {q}^{2} = 13q}$

$⟹</p><p>\bold{{q}^{2} - 13q + 22 = 0}$

$⟹</p><p>\bold{{q}^{2} - 11q - 2q + 22 = 0}$

$⟹</p><p>\bold{q(q - 11) - 2(q - 11) = 0}$

$⟹</p><p>\bold{(q - 2)(q - 11) = 0}$

$\bold{q = 2\: and\ \: q = 11}$

$\bold{\blue{Put\: these\: 2 \:values\: of \:q \:in \:equation (ii)}}$

we get two values of p =(2,11)

Now ,we have find out both values of p and q

$\bold{\pink{ {p}^{2} + {q}^{2} = {(11)}^{2} + {(2)}^{2} = 121 + 4}}$

$\bold{\orange{= 125}}$

Hence ,the value of p^2+q^2=125

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