Math, asked by navinpant123, 10 months ago

$if \: x - y = 8 \: and \: xy = 5 \: find \: {x }^{2} \: + {y}^{2}$

Answers

Answered by BihariSwag

$<body bgcolor="r"><font color="white">$

Given,

x - y = 8

xy = 5

(x - y)² = 8² = x² + y² - 2xy

64 = x² + y² - 2(5)

x² + y² - 10 = 64

x² +y² = 64 + 10

x² + y² = 74

Answered by umiko28

Answer:

${\huge{\overbrace{\underbrace{\purple{your \: answer:74}}}}}$

$<body bgcolor="pink"> \\ \bf\ \: \: we \: know \: that \\ \: \: \boxed{ \implies {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} } \\ \\ \: \: \: \bf\ here, \\ \: \: \bf\ x - y = 8 \\ \: \: \: \bf\ xy = 5 \\ \\ \: \: \bf\red{now,} \\ \bf\purple{ \implies : }{(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ \\ \bf\purple{ \implies: } {(x - y)}^{2} + 2xy = {x}^{2} + {y}^{2} \\ \\ \bf\purple{ \implies: } {(8)}^{2} + 2 \times 5 = {x}^{2} + {y}^{2} \\ \\ \bf\purple{ \implies: }64 + 10 = {x}^{2} + {y}^{2} \\ \\ \bf\purple{ \implies: }74 = {x}^{2} + {y}^{2} \\ \\ \: \: \bf\orange{ \boxed {\implies: {x}^{2} + {y}^{2} = 74}}$

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x² + y² = 74

$if \: x - y = 8 \: and \: xy = 5 \: find \: {x }^{2} \: + {y}^{2}$