Question

x2-x-a(a+1)=0 . please find the value of x .​

Answer 1

$\color{red}\large\underline{\underline{Question:}}$

$x^{2} - x - a(a + 1) = 0$

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$\color{purple}\large\underline{\underline{To\:Find:}}$

$\underline{The\:value\:of\:x}$

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$\color{orange}\large\underline{\underline{We\:Know:}}$

${\boxed{a^{2} - b^{2} = (a + b)(a - b)}}$

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$\color{Green}\large\underline{\underline{Solution:}}$

$x^{2} - x - a(a + 1) = 0$

$\Rightarrow x^{2} - x - a^{2} - a = 0$

$\Rightarrow x^{2} - a^{2} - a - x = 0$

$\Rightarrow (x - a)(x + a) - a - x = 0$

$\Rightarrow (x - a)(x + a) - 1(a + x) = 0$

$\Rightarrow (x + a)(x - a - 1) = 0$

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$\color{blue}\large\underline{\underline{Hence:}}$

$\underline{The\:value\:of\:x\:is}$

• $x + a = 0$

$\rightarrow x = - a$

• $x - a - 1 = 0$

$\rightarrow x = a + 1$

${\boxed{\therefore x = (a + 1); - a}}$

Answer 2

Step-by-step explanation:

here is your answer mate