Question

Solve for x:
6x^2-6(a+b)x+(4/3a^2+10/3ab+4/3b^2)=0​

Answer 1

Answer:

Step-by-step explanation:

6x^2-6(a+b)x + (12b^2+12a^2/9a^ 2b^2 +10/3ab)=0

6x^2 - 6(a+b)x + [12(a^2+b^2) + 30(a^2 b^2)/9(a^2 b^2)]=0

6x^2 - 6(a+b)x + [(12+30)(a^2+b^2)(a^2 b^2)/9(a^2 b^2)]=0

6x^2 - 6(a+b)x + [(42)(a^2+b^2)/9]=0

6x^2 - 6(a+b)x + 42a^2+42b^2/9=0

54x^2 - 54(a+b)x + 42a^2 + 42 b^2=0

9x^2 - 9(a+b)x + 6(a^2 + b^2)=0             - (div 6)

3x^2 - 3(a+b)x + 2(a^2 + b^2)=0

A= 3 B=-3(a+b) C=2(a^2+b^2)

D= B^2 - 4AC

D=[-3(a+b)]^2 - 4(3)[2(a^2+b^2)]

=9a^2 + 9b^2 +18ab - 24a^2 -24b^2

=18ab - 15a^2 - 15b^2