If a-1-a-2- find a4-1-a2A- 4B- 2C- 8D- 16

The correct option is B 2 Given a + 1/a = 2 Squaring on both sides we get (a+1/a)^2 = (2)^2 (a^2+1/a^2 + 2) = 4 (a^2+1/a^2) = 2 Taking LCM (a^2) on the LHS ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (x+y)^2

If a+1/a=2, f...

Question

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

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Solution

The correct option is B
2

Given
$a + \frac{1}{a} = 2$
Squaring on both sides we get
$(a + \frac{1}{a})^{2}$ = $(2)^{2}$
$(a^{2} + \frac{1}{a^{2}} + 2)$ = 4
$(a^{2} + \frac{1}{a^{2}})$ = 2
Taking LCM ( $a^{2}$ ) on the LHS we get
$\frac{a^{4} + 1}{a^{2}}$ = 2

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If a+1a=2 , find a4+1a2

The correct option is B 2 Given a+1a=2 Squaring on both sides we get (a+1a)2 = (2)2 (a2+1a2+2) = 4 (a2+1a2) = 2 Taking LCM (a2) on the LHS we get a4+1a2 = 2

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

The correct option is B
2

Given
$a + \frac{1}{a} = 2$
Squaring on both sides we get
$(a + \frac{1}{a})^{2}$ = $(2)^{2}$
$(a^{2} + \frac{1}{a^{2}} + 2)$ = 4
$(a^{2} + \frac{1}{a^{2}})$ = 2
Taking LCM ( $a^{2}$ ) on the LHS we get
$\frac{a^{4} + 1}{a^{2}}$ = 2