If the a -4- a -4- then what is the value of a 4-1- a 2 -A- 16-25

The correct option is A 16.25Given, a + 4/a= 4 a^2 + 4/a= 4 a^2 + 4 4a = 0 (a 2)^2= 0 a = 2 ∴ a^4 = 16 and a^2 = 4 The value of 16 + 1/4= 16 + 0.25 = 16.25 ...

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Byju's Answer

Standard VIII

Mathematics

Addition and Subtraction of Algebraic Expressions

If the a +4/ ...

Question

If the $a + \frac{4}{a} = 4$ , then what is the value of $a^{4} + \frac{1}{a^{2}}$ ?
16.25

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Solution

The correct option is A 16.25
Given,
$a + \frac{4}{a} = 4$
$\frac{a^{2} + 4}{a} = 4$
$a^{2} + 4 - 4 a = 0$
$(a - 2)^{2} = 0$
$a = 2$

$∴ a^{4} = 16 a n d a^{2} = 4$
The value of $16 + \frac{1}{4} = 16 + 0.25 = 16.25$

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If the a+4a=4, then what is the value of a4+1a2? 16.25

The correct option is A 16.25Given, a+4a=4 a2+4a=4 a2+4−4a=0 (a−2)2=0 a=2 ∴a4=16 and a2=4 The value of 16+14=16+0.25=16.25

If the $a + \frac{4}{a} = 4$ , then what is the value of $a^{4} + \frac{1}{a^{2}}$ ?
16.25

The correct option is A 16.25
Given,
$a + \frac{4}{a} = 4$
$\frac{a^{2} + 4}{a} = 4$
$a^{2} + 4 - 4 a = 0$
$(a - 2)^{2} = 0$
$a = 2$

$∴ a^{4} = 16 a n d a^{2} = 4$
The value of $16 + \frac{1}{4} = 16 + 0.25 = 16.25$