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**sunitaparija** 1.sqrt(x-2)+sqrt(x+3)=5

squaring both thr sides we have(sqrt(x-2)+sqrt(x+3))^2=25

using (a+b)^2 formula i.e a^2+ b^2+2ab here we get

x-2 +x+3 +2(sqrt(x-2)sqrt(x+3)0=25

2x+1-25 = -2sqrt(x-2)sqrt(x+3)

2(x-12)=-2sqrt(x-2)sqrt(x+3)

x-6 = -sqrt(x-2)sqrt(x+3)

taking square both the sides we have

(x-6)^2 = (-sqrt(x-2)sqrt(x+3))^2

x^2-12x+36 = (x-2)(x+3)

x^2-12x+36= x^2+x-6

taking the variables to the l.h.s and constants to r.h.s we have

-12x-x=-36-6

-13x = -42

-13x/-13= -42/-13

so,x =4

the next sum you can try similarly