Question

pleaseeeeeeeee solveeeee​

Answer 1

Answer:

p^2 +q^2= 125

Step-by-step explanation:

p+q=13

squaring both side

(p+q)^2=(13)^2

p^2 +q^2+2pq =169

putting the value of pq

p^2 +q^2+2×22 =169

p^2 +q^2+44=169

p^2 +q^2=169- 44

p^2 +q^2=125

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Answer 2

Step-by-step explanation:

a) Question:-

Given:-

$a - \frac{1}{a} = 4$

Find:-

$The \: value \: of \: \: {a}^{2} + \frac{1}{ {a}^{2} }$

Solution:-

Let's solve the problem,

We have

${a} - \frac{1}{a} = 4$

Squaring on both sides, we get

$\bigg(a - \frac{1}{a} \bigg)^{2} = (4 {)}^{2}$

✯Using algebraic identity

(x - y)² = (x - y)(x + y) = x² - 2xy + y²

Now,

$⟹ {a}^{2} - 2 \times a \times \frac{1}{a} + \bigg( \frac{1}{a} \bigg)^{2} = 16$

$⟹ {a}^{2} - 2 \times \cancel{a} \times \frac{1}{ \cancel{a}} + \frac{1}{ { a}^{2} } = 16$

$⟹ {a}^{2} - 2 + \frac{1}{ {a}^{2} } = 16$

$⟹ {a}^{2} + \frac{1}{ {a}^{2} } = 16 + 2$

$⟹ {a}^{2} + \frac{1}{ {a}^{2} } = 18$

So, the value of a²+1/a² is 18 Ans.

_________________________

b) Question:-

Given, p+q = 13 and Pq = 22

We know that, (p+q)² = p²+q²+2pq _____(1)

By putting the given value in equation (1),

(13)² = p² + q² + 2(22)

169 = p² + q² + 44

169 - 44 = p² + q²

125 = p² + q²

So, the value of p² + q² is 125 Ans.

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