Question

Qid : 62 - if a3 + b3 = 35 and ab = 6, then what is the value of a + b?3

Answer 1

☆☆your answer is here☆☆

solution:--

a³+b³=(a+b)³-3ab(a+b);
35=(a+b)³-3×6(a+b);
35=(a+b){(a²+2ab+b²)-18)
35=(a+b)(a²+b²)+12-18;
35=-6{a(a+b)+b(b-a)}(a+b)
41=a+b

Answer 2

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