Home
Class 12
MATHS
The equation (x+3-4(x-1)^(1//2))^(1//2)...

The equation `(x+3-4(x-1)^(1//2))^(1//2)+(x+8-6(x-1)^(1//2))^(1//2)=1` has (A) no solution (B) only `1` solution (C) only `2` solutions (D) more than `2` solutions

A

no solution

B

only `1` solution

C

only `2` solutions

D

more than `2` solutions

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Put `(x-1)^(1//2)=t`
or `x=t^(2)+1`
Therefore, the given equation becomes
`(t^(2)+4-4t)^(1//2)+(t^(2)+9-6t)^(1//2)=1`
`implies [(t-2)^(2)]^(1//2)+[(t-3)^(2)]^(1//2)=1`
`implies|t-2|+|t-3|=1`
This equation is satisfied for all values of `t` lying between `2` and `3` i.e.,
`2 le t le 3`
Thus, the given equation is satisfied for all values of `x` lying between `5` and `10`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

The equation sqrt(x+1)-sqrt(x-1)=sqrt(4x-1) has a.no solution b.one solution c. two solution d.more than two solutions

Find the values of a for which the equation x^(4)+(1-2a)x^(2)+a^(2)-1=0(A) has no real solutions (B) has one real solution (C) has two distinct real solutions (D) has three real solutions(E) has four distinct real solutions

The equation 2cos^(-1)x+s in^(-1)x=(11 pi)/(6) has a.no solution b.only one solution c .two solutions d.three solutions

The equation |x+1|^(log)_(("x"+1))(3+2-x^(2))=(x-3)|x| has a. unique solution b. two solutions c. no solution d. more than two solution

The solution of equation: |(x)/(x-1)|+|x|=(x^(2))/(|x-1|)

The solution of the equation 9^(x)-2^(x+(1)/(2))=2^(x+(3)/(2))-3^(2x-1)

Find values of k for which the equation |x^(2)-1]+x=k has (i) 4 solution (ii) 1 solution (ii) 3 solutions (iv) 2 solutions

|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 then the system of equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 has (A) no solution (B) one trivial and one non trivial solutions (C) only the trivial solution (0,0,0) (D) more than two solution

The equation (x^(2)+x+1)^(2)+1=(x^(2)+x+1)(x^(2)-x-5) for x in(-2,3) will have number of solutions.1 b.2 c.3d.0

The equation |((1+x)^2,(1-x)^2,-(2+x^2)),(2x+1,3x,1-5x),(x+1,2x,2-3x)|+|((1+x)^2,2x+1,x+1),((1-x)^2,3x,2x),(1-2x,3x-2,2x-3)|=0 has has (a) no real solution (b) 4 real solutions (c) two real and two non-real solutions (d) infinite number of solutions, real or non-real