If xy = 6 and x+y = 5 then the value of x^4
+ y^4 is :
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Answer:
xy=6 and x+y=5
$o, x⁴+y⁴
=(x²)² + (y²)²
We know that,
(x²)²+(y²)² +2x²y²=(x²+y²)²
(x²)²+(y²)²=(x²+y²)²-2x²y².........(i)
Similarly,
x²+y²+2xy = (x+y)²
x²+y²=(x+y)²-2xy
Putting values,
x²+y²=5²-12 =25-12=13...........(ii)
Comparing (i) and (ii),
x⁴+y⁴=13² - 2x²y²
= 169-2(xy)²
=169-2(6)²
=169-72
=97
Hope you got it.......
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