Question

a^2 + b^ 2 =88 and a*b =6. find a^ 3 + a^ 3​

Answer 1

Answer:

820

Step-by-step explanation:

a^2+b^2+2ab=(a+b)^2

so by putting value we get

a+b=10

a^3+b^3=(a+b)(a^2+b^2-ab)

by putting values we get

820

Answer 2

it is given that , a² + b² = 88 and a.b = 6....(1)

we know from algebraic identities,

a² + b² = (a + b)² - 2ab

so, a² + b² = (a + b)² - 2ab = 88

but a.b = 6

so, (a + b)² - 2(6) = 88

or, (a + b)² = 88 + 12 = 100

or, (a + b)² = (10)²

taking square root both sides,

(a + b) = ±10 .......(2)

we have to find a³ + b³

from algebraic identities

a³ + b³ = (a + b)³ - 3ab(a + b)

from equations (1) and (2),

= (10)³ - 3(6)(10) or, (-10)³ - 3(6)(-10)

= 1000 - 180 or, -1000 + 180

= 820 or, - 820

hence, a³ + b³ = 820 or -820