已知(25-x^2)^1/2-(15-x^2)^1/2=2,求(25-x^2)^1/2+(15-x^2)^1/2的值.

问题描述:

已知(25-x^2)^1/2-(15-x^2)^1/2=2,求(25-x^2)^1/2+(15-x^2)^1/2的值.

(25-x^2)^1/2-(15-x^2)^1/2=2
(25-x^2)^1/2=(15-x^2)^1/2+2
两边平方:25-x^2=15-x^2+4+4(15-x^2)^1/2
4(15-x^2)^1/2=6
两边平方:15-x^2=9/4
x^2=51/4
(25-x^2)^1/2+(15-x^2)^1/2
=(25-51/4)^1/2+(15-51/4)^1/2
=(49/4)^1/2+(9/4)^1/2
=9/2+3/2
=6