Math, asked by itgo10, 7 months ago

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

Answers

Answered by Anonymous
167

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\huge{\bold☘ }\mathfrak\pink{\bold{\underline{{ ℘ɧεŋσɱεŋศɭ}}}}{\bold☘}

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

\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer</p><p> }}}}}

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\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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Answered by ItzParth14
25

Answer:

p²+q² = (p+q)²-2pq

put the value ....

(13)²-2×22

169-44

125

Answer

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