Question

15. If x - y = 7 and xy = 9, find the value of (x²+ y²).​

Answer 1

Answer:

I'm happy to answer this

Answer 2

Given:-

• value of x - y = 7 and xy=9.

To Find:-

•Find the value of (x^2+y^2).

Solution:-

we have,

• x-y = 7
• xy=9

Using Formula:

$\: \: \sf \: ( {a}^{2} + {b}^{2} ) = {(a - b)}^{2} + 2ab$

Now substitute the given values,

$\: \: \sf( {x}^{2} + {y}^{2} ) = {(x - y)}^{2} + 2xy \\ \\ \: \: \sf \: = {(7)}^{2} + 2 \times 9 \\ \\ \: \: \sf \: = 49 + 18 \\ \\ \: \: \sf \: = 67$

Hence,the value of (x^2+y^2) is 67.

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Extra Info...

$\: \: \sf \implies \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ \: \: \sf \implies \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ \: \: \sf \: ( {a}^{2} - {b}^{2} ) = (a + b)(a - b)$