If the third term in the binomial expansion of $(1 + x^{l o g_{2} x})^{5}$ equals $2560$ , then a possible value of x is?

2 \sqrt{2}

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

\frac{1}{8}

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

4 \sqrt{2}

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

\frac{1}{4}

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

Open in App

Solution

The correct option is C $\frac{1}{4}$
$(1 + x^{l o g_{2} x})^{5}$
$T_{3} =^{5} C_{2} \cdot (x^{l o g_{2} x})^{2} = 2560$

$\Rightarrow 10 \cdot x^{2 l o g_{2} x} = 2560$
$\Rightarrow x^{2 l o g_{2} x} = 256$

$\Rightarrow 2 (l o g_{2} x)^{2} = l o g_{2} 256$
$\Rightarrow 2 (l o g_{2} x)^{2} = 8$

$\Rightarrow (l o g_{2} x)^{2} = 4$
$\Rightarrow l o g_{2} x = 2$ or $- 2$

$x = 4$ or $\frac{1}{4}$ .

Suggest Corrections

Similar questions

If the third term in the binomial expansion of $(1 + x)^{m}$ is - $\frac{1}{8} x^{2}$ , then the rational value of m is

If the third term in the binomial expansion of $(1 + x)^{m} i s - x^{2}$ , then the rational value of m is

If the third term in the binomial expansion of $(1 + x)^{m}$ is $- \frac{1}{8} x^{2}$ , then the rational value of m is

(1 + x)^{n}

n^{2} - 9 n

{(3^{5 x / 4} + 3^{- x / 4})}^{n}

64

(n - 1),

x

Join BYJU'S Learning Program