Question

If X + y is equal to 7 and X square + y square is equal to 25 then find the value of x cube + y cube

Nnnsol

Answer 1

Explanation:

Solution

Given :-

x + y = 7 _______(1)

x² + y² = 25________(2)

Find :-

Value of x³ + y³

Explanation

Using Formula

★ (x²+y²) = (x+y)² - 2xy

So,

➡ 25 = (7)² - 2xy

➡25 - 49 = -2xy

➡2xy = 49-25

➡2xy = 24

➡xy = 24/2

➡xy = 12 _____________(3)

Now,

★ (x-y) = (x+y)² - 4xy

➡ x - y = (7)² - 4×12

➡x - y = 49 - 48

➡x - y = 1 ____________(4)

Add equ(1) & equ(4)

➡2x = 8

➡x = 8/2

➡x = 4

Keep value of x in equ(1)

➡4 + y = 7

➡y = 7 - 4

➡y = 3

Hence

Value of x = 4

Value of y = 3

Since

Value of x³ + y³ = 4³ + 3³ = 64 + 27 = 91

________________

Answer 2

Explanation:

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