Home
Class 12
MATHS
Find all possible values of the followin...

Find all possible values of the following expressions :
` sqrt(x^(2)-9) `

Text Solution

Verified by Experts

(i) `sqrt(x^(2)-4)`
Least value of square root is 0 when `x^(2)=4 " or " x= +-2.` Also `x^(2)-4 ge 0`
Hence, `sqrt(x^(2)-4) in [0, oo).`
(ii) `sqrt(9-x^(2))`
Least value of square root is 0, when `9-x^(2)=0` or `x= +-3.`
Also, the greatest value of `9-x^(2)` is 9, when `x = 0`.
Hence, we have `0 le 9 - x^(2) le 9 impliessqrt(9-x^(2)) in [0,3].`
(iii)`sqrt(x^(2)-2x+10)=sqrt((x-1)^(2)+9)`
Here, the least value of `sqrt((x-1)^(2)+9)` is 3 , when `x-1=0`.
Also `(x-1)^(2)+9 ge 9impliessqrt((x-1)^(2)+9) ge 3`
Hence, `sqrt(x^(2)-2x+10) in [3, oo).`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find all the possible the value of the following expression dot sqrt(x^2-4) (ii) sqrt(9-x^2) (iii) sqrt(x^2-2x+10)

Find all the possible values of the following expressions: 1/(x^2+2) (ii) 1/(x^2-2x+3) (iii) 1/(x^2-x-1)

Find all the possible values of the expression: 1/(x^2+2)

Find all possible values of sqrt(|x|-2)

Find all the possible values of the expression sqrt(x^2-4) .

Find all possible values of expressions (2+x^2)/(4-x^2)

Find all the possible values of 1/x for x>3 .

Find all possible values of expression sqrt(1-sqrt(x^(2)-6x+9)).

Find all possible values ( range) of the quadratic expression: 1+6x -x^2 , when x in [-3,2] .

Find all the possible values of expression : ( |x|)/(x) + (|y|)/y