Question

If x+y=4 & xy=45 then find the value of x³-y³?

Solve this fast📝

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Answer 1

Solution:

There will be a slight change in the question. The given portion will be (x-y) = 4 instead of x+y=4

Given x - y = 4 and xy = 45

Squaring both sides

or, (x - y)^2 = 16

or, x^2 + y^2 - 2xy = 16

or, x^2 + y^2 - 2.45 = 16

or, x^2 + y^2 - 90 = 16

or, x^2 + y^2 = 90+16

or, x^2 + y^2 = 106 ---- (1)

We know that:
x^3-y^3 = (x-y)(x^2+y^2+xy)

Putting the above values in the formula:

= 4(106 + 45)

= 4(151)

= 604 (Answer)