Question

已知√(25-x^2)-√(15-x^2)=2,求√(25-x^2)+2√(15-x^2)的值

Answer 1

√(25-x^2)-√(15-x^2)=2

√(25-x^2)=2+√(15-x^2)

两边平方

25-x^2=4+4√(15-x^2)+15-x^2

√(15-x^2)=3/2

15-x^2=9/4

x^2=51/4

√(25-x^2)+2√(15-x^2)

=√(49/4)+2√(9/4)

=7/2+3

=13/2