Question

已知√7x²+9x=13+√7x²-5x+13=7x,求x的值

Answer 1

设√(7x^2+9x+13)-√(7x^2-5x+13)=a(1)

√(7x^2+9x+13)+√(7x^2-5x+13)=7x(2)

(1)*(2)得

14x=7ax

a=2

√(7x^2+9x+13)-√(7x^2-5x+13)=2

(1)+(2)

2√(7x^2+9x+13)=7x+2

28x^2+36x+52=49x^2+28x+4

21x^2-8x-48=0

(3x+4)(7x-12)=0

x1=-4/3,x2=12/7