Question

solve using factorization.
x² - 4ax + 4a² - b² = 0​

Answer 1

Answer:

x^2-4ax+4a^2-b^2=0

1st - method:-

(x^2-4ax+4a^2)-b^2=0

or. (x-2a)^2-(b)^2=0

or. (x-2a+b).(x-2a-b)=0

Either. (x-2a+b)=0. => x=2a-b

Or. (x-2a-b)=0. =>. x=2a+b

Thus , x=2a-b. , 2a+b. Answer

2nd - method:-

x^2-4ax+4a^2-b^2=0

or. x^2-4a.x+(2a+b).(2a-b)=0

or. x^2–{(2a+b)+(2a-b)}.x+(2a+b).(2a-b)=0

or. x^2-(2a+b).x-(2a-b).x+(2a+b).(2a-b)=0

or. x(x-2a-b)-(2a-b).(x-2a-b)=0

or. (x-2a-b).(x-2a+b)=0

or. x=2a+b. , 2a-b. Answer.

Step-by-step explanation:

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Answer 2

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$\sf{x^2-4ax+4a^2-b^2=0}\\\\\sf{\to (x)^2-2 * 2a * x+(2a)^2-b^2=0}\\\\\sf{\to (x-2a)^2-b^2=0 }\\\\\sf{\to (x-2a)^2=b^2}\\\\\sf{\to (x-2a)=b}\\\\\sf{\to x=b+2a}$

Hence, the value of x is 2a + b.

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Identity used :-

$\bullet \sf{(a-b)^2=(a)^2+(b)^2-2\times a \times b}$