Question

Find the roots of ax2 +a = a2x+x by formula method

Answer 1

Answer:

1/(a+b+x)=1/a + 1/b + 1/x

1/(a+b+x)=(bx+ax+ab)/abx

abx=abx+a2x+a2b+b2x+abx+ab2+bx2+ax2+abx

ax2+bx2+a2x+abx+abx+b2x+a2b+ab2=0

x2(a+b)+ax(a+b)+bx(a+b)+ab(a+b)=0

(a+b)(x2+ax+bx+ab)=0

since, a+b!=0

so, x2+ax+bx+ab=0

x(x+a)+b(x+a)=0

(x+a)(x+b)=0

x=-a,-b

Answer 2

$given, \: ax {}^{2} + a = a {}^{2} x + x \\ = > ax {}^{2} + a - a {}^{2} x - x = 0 \\ = > ax {}^{2} - a {}^{2} x - x + a = 0 \\ = > ax(x - a) - 1(x - a) = 0 \\ = > x - a = 0 \: or \: ax - 1 = 0 \\ = > x = a \: or \: x = \frac{1}{a} \\ hence, \: the \: required \: roots \: of \: the \: given \: equation \: are \: a \: and \: \frac{1}{a}$