If a-1-2-4- then a-1-a2-A- 14B- 16C- 64D- 18

The correct option is A 14 If a + 1/a = 4 , then a^2 + 1/a^2 = ____________ Given that a + 1/a = 4 Squaring on both sides , we have (a + 1/a)^2 = 4^2 a^2 + ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Expansion of (x+y)^2

If a+1/2=4, t...

Question

If $a + \frac{1}{a}$ = 4 , then $a + \frac{1}{a^{2}}$ = ____________

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

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

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

Open in App

Solution

The correct option is B
14

If $a + \frac{1}{a}$ = 4 , then $a^{2} + \frac{1}{a^{2}}$ = ____________

Given that $a + \frac{1}{a}$ = 4
Squaring on both sides , we have

$(a + \frac{1}{a})^{2}$ = $4^{2}$

$a^{2} + 2 a \times \frac{1}{a} + \frac{1}{a^{2}}$ = 16

$a^{2} + \frac{1}{a^{2}} + 2$ = 16

$∴$ $a^{2} + \frac{1}{a^{2}}$ = 16 -2
= 14

Hence $a^{2} + \frac{1}{a^{2}}$ = 14

Suggest Corrections

Similar questions

Q. If (2,2) lies on

4 x + 5 y = k

, the value of

k

= ______.

Question 13

Cube of $(\frac{- 1}{4}) i s$
(a) $\frac{- 1}{12}$
(b) $\frac{1}{16}$
(c) $\frac{- 1}{64}$
(d) $\frac{1}{64}$

If $a - \frac{1}{a}$ = 4 , then $a^{2} + \frac{1}{a^{2}}$ = 16

If A is a square matrix such that $A (A d j . A) = ⎡ ⎢ ⎣ \begin{matrix} 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦,$ then $\frac{| a d j (a d j . A) |}{| a d j . A |}$ is equal to

$If x = 9 + 4 \sqrt{5}, then \sqrt{x} - \frac{1}{x} =$ _______.

Join BYJU'S Learning Program

If a+1a = 4 , then a+1a2 = ____________

The correct option is B 14 If a+1a = 4 , then a2+1a2 = ____________ Given that a+1a = 4 Squaring on both sides , we have (a+1a)2 = 42 a2+2a×1a+1a2 = 16 a2+1a2+2 = 16 ∴ a2+1a2 = 16 -2 = 14 Hence a2+1a2 = 14

If $a + \frac{1}{a}$ = 4 , then $a + \frac{1}{a^{2}}$ = ____________