Question

if x²+y²=13 and xy=6, find the value of the following:
i) x+y

ii) x-y

iii) x⁴+y⁴

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Answer 1

Answer:

i)x+y=5

i)x+y=5ii)x-y=1

i)x+y=5ii)x-y=1iii)x⁴+y⁴=97

Step-by-step explanation:

x²+y²+2xy=13+12

25=(x+y)²

i)x+y=5

x²+y²-2xy=13-12

(x-y)²=1

ii)x-y=1

(x²+y²)²=x⁴+y⁴+2(xy)²

x⁴+y⁴=(x²+y²)²-2(xy)²

x⁴+y⁴=169-72

iii)x⁴+y⁴=97