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Solve the following inequations -
(a) (x -1)( x2 – x – 2 )1/2 = 0

(b)( 2 – x – x2 )1/2=  x – 4
5 years ago

(x-1)(x2-x-2)1/2=0
=>either x-1=0 or(x2-x-1)1/2=0
if x-1=0 then x=1
and if (x2-x-1)1/2 =0 then
x2-x-1=0 and x2-x-1>/0
=> (x-2)(x+1)=0 and(x-2)(x+1)>/0
=>x=2,-1 and x=-1 or x=2
so we ox=2 and -1
so total values of x=-1,2,1

Thanks & Regards
Rinkoo Gupta

5 years ago IIT Delhi
174 Points
(a) x=1, -1, 2 are satisfying the function
but x2–x –2>=0
so x belongs to (-infinite ,-1]U[2,infinte)
so x=-1 and x=2 are solutions

(b)-x2–x +2>=0
-2 and 1 satisfies the equation so x belong to [-2,1]
squaring both sides
2 – x – x2=x2-8x+16
=>2x2-7x+14=0 D<0 so no solution

5 years ago
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