Question

x square + y square = 49
x-y=3
find x cube - y cube
plss help fast pls

Answer 1

ANSWER:

• Value of x³-y³ = 207

GIVEN:

• x²+y² = 49 .....(i)
• x-y = 3

TO FIND:

• x³-y³

SOLUTION:

Formula:

=> (x-y)² = x²+y²-2xy

Here:

=> x-y = 3

Squaring both sides we get;

=> (x-y)² = (3)²

=> x²+y²-2xy = 9

=> 49-2xy = 9. [From (i)]

=> -2xy = 9-49

=> xy = -40/(-2)

=> xy = (20)

Formula:

=> (x³-y³) = (x-y)(x²+y²+xy)

Now using this formula:

=> (x³-y³) = (x-y)(x²+y²+xy)

Putting the values we get;

=> (x³-y³) = 3[49+20]

=> (x³-y³) = 3(69)

=> x³-y³ = 207

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab