Question

the sum of two numbers is 9 and their product is 20. Find the sum of their cubes​

Answer 1

Answer:

189

Step-by-step explanation:

Let two number be x and y

Given,x+y=9 and xy=20

Now,x+y=9

Squaring both the sides,

(x+y)

2

=9

2

=>x

2

+y

2

+2xy=81

=>x

2

+y

2

+2(20)=81

=>x

2

+y

2

+40=81

=>x

2

+y

2

=81−40

=>x

2

+y

2

=41

Now,

x

3

+y

3

=(x+y)(x

2

−(x)(y)+y

2

)

=(9)(41−20)

=9(21)

=189

Answer 2

Let two number be x and y

Given,x+y = 9 and xy = 20

Now,x+y = 9

Squaring both the sides,

(x + y)² = 9²

=> x² + y² + 2xy = 81

=> x² + y² + 2(20) = 81 => x² + y² + 40 = 81

=> x² + y² = 81 - 40

=> x² + y² = 41

Now,

x³ + y³ = (x + y) (x² − (x)(y) + y²)

= (9)(41 - 20)

= 9(21)

Answer = 189

Hope you understand :))