√(x²+17)+√(15-x²)=6,求√(x²+17)-√(15-x²)

√(x²+17)+√(15-x²)=6,求√(x²+17)-√(15-x²)
√(x²+17)+√(15-x²)=6,求√(x²+17)-√(15-x²)

√(x²+17)+√(15-x²)=6,求√(x²+17)-√(15-x²)
设A=根号（X^2+17),B=根号（15-x^2)
A+B=6
(A+B)^2=36
A^2+2AB+B^2=36
X^2+17+2AB+15-X^2=36
2AB=4
(A-B)^2=A^2-2AB+B^2=X^2+17-4+15-X^2=28
即原式=A-B=2根号7,(由于A>B,故A-B >0)