Question

solve the equation
1 upon a+b+x=1 upon a+1/b+1/x

Answer 1

1/a+b+x = 1/a + 1/b +1/x
1/a +b +x - 1/x = 1/a +1/b
x-a -b -x/ax + bx +x^2 = b+a/ab
-(a+b)/ax + bx +x^2 = b+a /ab
-1/ax +bx+x^2 =1/ab
-ab= x^2+ax+bx
x^2 +(b+a)x+ ab=0
here, a=1, b=(b+a), c=ab
by quadratic formula,
D= b^2 - 4ac
=(b+a)^2 - 4(1)(ab)
=a^2 +b^2 + 2ab -4ab
=a^2 + b^2 - 2ab = (a-b)^2
so, x = -b ± root b^2 -4ac /2a
= -(a+b)±root (a-b)^2 /2(1)
= -a-b+a-b/2 , -a-b-a+b/2
= -2b/2 , -2a/2
= -b, -a