Question

If $a-b=5$, and $ab=6$, find the value of $(a^2+b^2)(a^3-b^3)$

• A. 8000
• B. 8754
• C. 7955
• D. 7099

Answer 1

The correct option is C

7955

Given: $a-b=5$ ... (i)

$ab=6$ ... (ii)

Squaring equation (i), we get

$(a-b{)}^2=25$

$\Rightarrow a^2+b^2-2ab=25$

$\Rightarrow a^2+b^2-2\times 6=25$

$\Rightarrow a^2+b^2=25+12=37$ ... (iii)

Cubing equation (i), we get

$(a-b{)}^3=125$

$\Rightarrow a^3-b^3-3ab(a-b)=125$

$\Rightarrow a^3-b^3-3\times 6\times 5=125$

$\Rightarrow a^3-b^3=125+90=215$ ... (iv)

Now,

$(a^2+b^2)(a^3-b^3)=37\times 215=7955$