Question

x3+y3=35, x+y=5 find x4+y4=?
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Answer 1

Answer:

I hope it helps you.

Step-by-step explanation:

We know that

x3 + y3 = (x + y)(x2 + y2 – xy)

Now we have x3 + y3 = 22 and x + y = 5

⇒ 22 = 5(x2 + y2 – xy)

⇒ 22 = 5[(x + y)2 − 3xy)]

⇒ 22 = 5[(5)2 − 3xy)]

⇒ xy = 103/15

Now multiply x3 + y3 = 22 with x + y = 5

⇒ x4 + y4 + xy(x2 + y2) = 110

⇒ x4 + y4 = 110 – xy{(x2 + y2 − 2xy + 2xy)}

⇒ x4 + y4 = 110 – xy{(x + y)2 − 2xy}

xy = 103/15 and x + y = 5

⇒ x4 + y4 = 110 – 103/15{(5)2 − 2 × 103/15}

⇒ x4 + y4 = 110 – 6.87{(25 – 2 × 13.73}

⇒ x4 + y4 = 126.9 ~ 127

∴ Value of x4 + y4 is 127