Question

If a3 + b3 = 35 and ab = 6, then what is the value of a + b?

Answer 1

Answer:

Thus the value of a + b is 5

To find:

Value of a + b = ?

Solution:

Given : $a^3 + b^3 = 35$ and $ab = 6$

Let us take the value of $(a+b)=x$

We know that the value of  

$( a + b ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + 3 a b ( a + b )$

Substituting (a + b) = x in the above expression, we get,

$( x ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + 3 a b ( x )$

Substituting the value of $ab = 6$ and $a^3 + b^3 = 35$ in the above derived expression

$\begin{array} { c } { x ^ { 3 } = 35 + 3 \times 6 ( x ) } \\\\ { x ^ { 3 } = 35 + 18 x } \\\\ { x ^ { 3 } - 18 x = 35 } \\\\ { x \left( x ^ { 2 } - 18 \right) = 35 } \\\\ { x \left( x ^ { 2 } - 18 \right) = 5 \times 7 } \end{array}$

Let us take

$x=5$

And

$\begin{array} { c } { x ^ { 2 } - 18 = 7 } \\\\ { x ^ { 2 } = 7 + 18 } \\\\ { x ^ { 2 } = 25 } \\\\ { x = 5 } \end{array}$

Thus, the value of x is 5.

$x=a+b=5$

Thus, the value of a + b is equal to 5

Answer 2

Answer:

a+b = 5

Step-by-step explanation:

$Given \: a^{3}+b^{3}=35$----(1)

$and\\ ab = 6 ----(2)$

/* By algebraic identity:

$\boxed { (a+b)^{3}=a^{3}+b^{3}+3ab(a+b)}$*/

Now ,

$(a+b)^{3}=35+3\times6(a+b)$

=$35+18(a+b)$

Let (a+b) = x , we get

$x^{3}=35+18x$

if x = 5 ,

5³=35+18×5

=> 125 = 35 + 90

=> 125 = 125 (true)

Therefore,

x = (a+b) = 5

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