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

Answer 1

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

Given:-

• x + y = 7
• x² + y² = 25

To Find: Value of (x³ + y³).

We know,

a² + b² = (a + b)² - 2ab

similarly,

x² + y² = (x + y)² - 2xy

→ 25 = 7² - 2xy

→ - 2xy = 5² - 7²

→ - 2xy = (5 + 7)(5 - 7)

→ 2xy = (12)(2)

→ xy = 12

Also, we know,

a³ + b³ = (a + b)³ - 3ab(a + b)

→ x³ + y³ = (x + y)³ - 3xy(x + y)

= (7)³ - 3(12)(7)

= 343 - 252

= 91 (Answer)