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Power growth (Posted on 2023-11-26)

If x+y=4 and x³+y³=18, find the value of x⁵+y⁵.

No Solution Yet Submitted by Danish Ahmed Khan

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Algebraic Solution

Comment 3 of 3 |

x^3+y^3 = (x+y)(x^2 - xy + y^2) = 4(x^2 - xy + y^2) = 18 (eqn 1)

(x+y)^2 = 16 = x^2 + 2xy + y^2 (eqn 2)

x^2 - xy + y^2 = 18/4 (eqn 1)

x^2 + 2xy + y^2 = 16 (eqn 2) subtract (1) from (2)

3xy = 23/2

xy = 23/6

x^2 + y^2 = 16 - 23/3 = 25/3

(x^2 + y^2)(x^3+y^3) = x^5 + y^5 + (x+y)(x^2y^2)

(25/3) * (18) = (x^5 + y^5) + (4) * (23/6)^2

150 = (x^5 + y^5) + (2116 / 36)

(x^5 + y^5) = 3284/36 = 821/9 = 91 2/9

Posted by Larry on 2023-11-26 10:36:27

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