Question

If x^2+y^2=58 and x+y=10 then find value of x^3+y^3

Answer 1

Hey! Here's your answer!

x + y = 10

x = y - 10

(y - 10)^2 + y^2 = 58

y^2 - 20y + 100 + y^2 = 58

2y^2 - 20y + 42 = 0

2y^2 - 6y - 14y + 42 = 0

2y(y - 3) - 14(y - 3) = 0

y = 7 or y = 14

x = 3 or x = -4

Say, x = 3 and y = 7,

x^3 + y^3 = 3*3*3 + 7*7*7

                = 27 + 343

x^3 + y^3 = 370

Hope this helps! :)

Answer 2

HELLO USER :-) HERES UR ANSWER

x^3+y^3= (x+y)(x^2-xy+y^2)
= (10)(58-xy)
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NOW WE NEED TO FIND xy
WE KNOW:-
(x+y)^2= x^2+y^2+2xy
100=58+2xy
42=2xy
21=xy
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NOW COMING BACK TO x^3+y^3
x^3+y^3=(10)(58-xy)
=(10)(58-21)
=(10)(37)
=10×37
=370


SO THE ANSWER IS 370
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