(1 2a)^2 4(1 a)^2=0 ⇒ (1 2a)^2 (2 2a)^2=0 (a^2 b^2=(a b)(a+b)) (1 2a+2 2a)(1 2a (2 2a))=0 ⇒ (3 4a)(1 2a 2+2a)=0 ⇒ (3 4a)( 1)=0 ...

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Byju's Answer

Standard VIII

Mathematics

Properties of Square Numbers

1-2a2=41-a2

Question

$(1 - 2 a)^{2} = 4 (1 - a)^{2}$

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Solution

$(1 - 2 a)^{2} - 4 (1 - a)^{2} = 0$
$\Rightarrow (1 - 2 a)^{2} - (2 - 2 a)^{2} = 0$ $(a^{2} - b^{2} = (a - b) (a + b))$
$(1 - 2 a + 2 - 2 a) (1 - 2 a - (2 - 2 a)) = 0$
$\Rightarrow (3 - 4 a) (1 - 2 a - 2 + 2 a) = 0$
$\Rightarrow (3 - 4 a) (- 1) = 0$
$\Rightarrow 3 - 4 a = 0$
$\Rightarrow a = \frac{3}{4}$ .

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(1−2a)2=4(1−a)2

(1−2a)2−4(1−a)2=0⇒(1−2a)2−(2−2a)2=0 (a2−b2=(a−b)(a+b))(1−2a+2−2a)(1−2a−(2−2a))=0⇒(3−4a)(1−2a−2+2a)=0⇒(3−4a)(−1)=0⇒3−4a=0⇒a=34.

$(1 - 2 a)^{2} = 4 (1 - a)^{2}$