Question

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

Answer 1

Given That

• x-y=7
• xy=9

To Find

• (x²+y²)

Solution

$\mathfrak{As\ We\ kno that}$

$\sf{→(x-y)²=x²+y²-2xy}$

$\sf→7²=x²+y²-2×9$

$\sf →x²+y²=49+18$

$~~~~~~~\bf x²+y²=67$

More Useful Identity

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

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

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

$\sf(a + b + c)^{2} = {a}^{2} + {b}^{2} + {c}^{2} 2ab + 2bc + 2ca$

$\sf(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b)$

$\sf(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b)$

$\sf a ^{3} + {b}^{3} = (a + b)(a ^{2} + {b}^{2} - ab)$

$\sf a ^{3} - {b}^{3} = (a - b)(a ^{2} + {b}^{2} + ab)$

Answer 2

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