Question

solve 9x^2-3(a^2+b^2)x+a^2b^2 by quadratic formula​

Answer 1

9x2 - 9(a + b)x + (2a2 + 4ab + ab + ab2) = 0 9x2 - (9a + 9b)x + [2a(a + 2b) + b(a + 2b)] = 0 9x2 - (9a + 9b)x + [(a + 2b)(2a + b)] = 0 9x2 - 3[(a + 2b) + (2a + b)]x + {(a + 2b)(2a + b)} = 0 9x2 - 3(a + 2b)x - 3(2a + b)x + {(a + 2b)(2a + b)} = 0 3x[3x - (a + 2b)] - (2a + b)[3x +(a - 2b)] = 0 [3x - (a + 2b)][3x -(2a + b)] = 0 [3x - (a + 2b)][3x - (2a + b)] = 0 [3x - (a + 2b)] = 0  or we can have [3x - (2a + b)] = 0 3x = (a + 2b) or 3x = (2a + b) Hence, x =  a + 2 b 3 a+2b3 or x =  2 a + /29164/solve-the-following-quadratic-equation-9x-2-9-a-b-x-2a-2-5ab-2b-2-00

Consider the equation 9x2−9(a+b)x+[2a2+5ab+2b2]=0

Now comparing with Ax2+Bx+C=0 we get

A=9,B=−9(a+b) and C=(2a2+5ab+2b2)

Now discriminant

D=B2−4AC

={−9(a+b)}2−4×9(2appp2+5ab+2b2)=92(a+b)2−4×9(2a2+5ab+2b2)

9[9(a+b)2−4(2a2+5ab+2b2]=9[9a2+9b2+18ab−8a2−20ab−8b2]

9(a2+b2−2ab)=9

i hope you this will help u but ans is correct