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Ira Lisetskai [31]
4 years ago
8

If (x-y)^2=71 and x^2+y^2=59 what is the value of xy?

Mathematics
1 answer:
Lena [83]4 years ago
5 0
Solve the equations
first one
take the sqrt of both sides
x-y=√71
add y to both sides
x=y+√71
sub y+√71 for x in other part


(y+√71)²+y²=59
y²+2y√71+71+y²=59
2y²+2y√71+71=59
minus 59 both sides
2y²+2y√71+12=0
factor out 2
2(y²+y√71+6)=0
use quadratic equation or something
y=\frac{- \sqrt{71}- \sqrt{47}  }{2} and \frac{- \sqrt{71}+ \sqrt{47}  }{2}

sub those for x

x=y+√71
note: √71=(2√71)/2

x=\frac{- \sqrt{71}- \sqrt{47}  +2\sqrt{71}}{2} ,\frac{\sqrt{71}- \sqrt{47}}{2}
or
x=\frac{- \sqrt{71}+ \sqrt{47}  +2\sqrt{71}}{2} ,\frac{\sqrt{71}+ \sqrt{47}}{2}

xy=\frac{\sqrt{71}- \sqrt{47}}{2}  times \frac{-\sqrt{71}- \sqrt{47}}{2} or \frac{\sqrt{71}+ \sqrt{47}}{2}  times \frac{-\sqrt{71}+ \sqrt{47}}{2}

the result is -6 both times

xy=-6
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