Question 20If 49x2-b- 7x-1-2 7x-1-2 -then the value of b isA 0B 1-2C 1-4D 1-2

Given, nbsp;(49x^2 b)= ( 7x+1/2 ) ( 7x 1/2 ) ⇒ [49x^2 (√(b))^2]= [ (7x)^2 ( 1/2 ) ^2 ] [using identity, (a+b)(a b)=a^2 b^2] ⇒ 49x^2 (√(b))^2=49x^2 ( 1/ ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity: (a - b)^2 = a^2 + b^2 - 2ab

Question 20If...

Question

Question 20
If $49 x^{2} - b = (7 x + \frac{1}{2}) (7 x - \frac{1}{2})$ ,
then the value of b is

A) $0$
B) $\frac{1}{\sqrt{2}}$
C) $\frac{1}{4}$
D) $\frac{1}{2}$

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Solution

Given,
$(49 x^{2} - b) = (7 x + \frac{1}{2}) (7 x - \frac{1}{2})$
$\Rightarrow [49 x^{2} - (\sqrt{b})^{2}] = [(7 x)^{2} - {(\frac{1}{2})}^{2}] [u s i n g i d e n t i t y, (a + b) (a - b) = a^{2} - b^{2}]$
$\Rightarrow 49 x^{2} - (\sqrt{b})^{2} = 49 x^{2} - {(\frac{1}{2})}^{2}$
$\Rightarrow - (\sqrt{b})^{2} = - {(\frac{1}{2})}^{2}$
$\Rightarrow (\sqrt{b})^{2} = - {(\frac{1}{2})}^{2}$ [multiplying both sides by -1]
$∴ b = \frac{1}{4}$
The answer is C.

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Similar questions

Q. Question 20
If

49 x^{2} - b = (7 x + \frac{1}{2}) (7 x - \frac{1}{2})

,
then the value of b is

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Q. If

49 x^{2} - b = (7 x + \frac{1}{2}) (7 x - \frac{1}{2})

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Question 4
If $\frac{1}{2}$ is a root of equation $x^{2} + k x - \frac{5}{4} = 0$ , then the value of k is
$(A) 2$
$(B) - 2$
$(C) \frac{1}{4}$
$(D) \frac{1}{2}$