Question

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If x3 + y3 = 72 and xy = 6 then find x-y =?,x is greater than y

Answer 1

i think the question is wrong . but if we consider x3 and y3 as x [power]3 and y[power] 3 then we have solutions:

x3+y3=72 xy=8

Notice,

(x+y)3=x3+y3+3xy(x+y) (x+y)3=72+3(8)(x+y) (x+y)3−24(x+y)−72=0

Above is the cubic equation in terms of (x+y)

which has one real root 6 Hence, we get x+y=6

Now,

(x−y)2=(x+y)2−4xy (x−y)=±(x+y)2−4xy‾‾‾‾‾‾‾‾‾‾‾‾‾√ x−y=±(6)2−4×8‾‾‾‾‾‾‾‾‾‾‾√ =±4‾√=±2 Hence, we have x−y=±2