Question

if a+b=8,ab=16 then the value of a³+b³ is​

Answer 1

Answer:

The answer is 128

Step-by-step explanation:

Using the algebraic identity

     $(a+b)^3=a^3+b^3+3ab(a+b)$

     $\Rightarrow 8^3=a^3+b^3+3(16)(8)$, substitute the given values

    $\Rightarrow 512=a^3+b^3+384\\\therefore a^3+b^3=512-384=128$

Answer 2

Given: a+b = 8

ab = 16

To find: The value of a^3 + b^3

Solution:

As we know,

According to algebraic identity

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

Simplifying the above equation.

We take out 3ab common from the last two terms.

Now we get,

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

As given in the question,

a+b = 8

ab = 16

Putting these values in the above equation.

We get,

(8)^3 = a^3 + b^3 +3(16)(8)

512 = a^3 + b^3 + 384

a^3 + b^3 = 512- 384

a^3 + b^3 = 128

Hence, The value of a^3 + b^3 = 128