If $a^{3} = 117 + b^{3}$ and $a = 3 + b$ , then the value of $a + b$ is:

\pm 7

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

49

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\pm 13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\pm 7$
$a^{3} = 117 + b^{3}$ $\Rightarrow$ $a^{3} - b^{3} = 117$
$a = 3 + b$ $\Rightarrow$ $a - b = 3$
Now, ${(a - b)}^{3} = a^{3} - b^{3} - 3 a b (a - b)$ d
$\Rightarrow$ $3^{3} \times 3$
$\Rightarrow$ $27 = 117 - 9 a b$ $\Rightarrow$ $9 a b = 90$ $\Rightarrow$ $a b = 10$
$∴$ Using the identity ${(a + b)}^{2} = {(a - b)}^{2} + 4 a b$ , we have
${(a + b)}^{2} = 3^{2} + 4 \times 10 = 9 + 40 = 49$
$\Rightarrow$ $a + b = \sqrt{49} = \pm 7$

Suggest Corrections

Similar questions

a - b = 3

a^{3} - b^{3} = 117

a + b

If $a - b = 3$ and $a^{3}$ - $b^{3}$ $= 117$ ,then $a b$ = _________

If the value of $(\frac{a^{3} - b^{3}}{a^{3} + b^{3}})$ when a = 7 and b = 2 is $\frac{335}{p}$ , then p is 321.

If the value of $(\frac{a^{3} - b^{3}}{a^{3} + b^{3}})$ , when $a = 7$ and $b = 2$ is $\frac{335}{p}$ , then $p$ is $321$ .

\frac{a}{b} = \frac{7}{3}

\frac{a^{3} - b^{3}}{b^{3}}

Join BYJU'S Learning Program