Hailie Blevins

Hailie Blevins

Answered

2022-06-25

How to solve the following pair of non-linear equations
x 3 + y 3 = 152 x 2 y + x y 2 = 120

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Answer & Explanation

America Barrera

America Barrera

Expert

2022-06-26Added 23 answers

Multiply by three the second equation and add this to the first one, and you'll get
( x + y ) 3 = 152 + 360 = 512 = 2 9 x + y = 2 3 = 8
Now take it from here.

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Lydia Carey

Lydia Carey

Expert

2022-06-27Added 9 answers

Another method:
Suppose x , y be the roots of z 2 + a z + b = 0
x + y = a and x y = b
x 3 + y 3 = ( x + y ) 3 3 x y ( x + y ) = a 3 + 3 a b = 152
x y ( x + y ) = a b = 120
a 3 = 152 3 120 = 512
b = 120 / 8 = 15
Solve of z 2 8 z + 15 = 0 for x and y

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