Home
Class 12
MATHS
The number of integral value of x satist...

The number of integral value of `x` satistying `sqrt( x^2+10 x-16)

Text Solution

Verified by Experts

The correct Answer is:
3
`sqrt(-x^2+10x-16) lt x-2 `
We must have `-x^2+10 x -16 gt 0 `
or `x^2- 10 x+16 le 0 `
`rArr 2 le x le 8 `
Also `-x^2+10x- 16 lt x^2 -4x +4`
or `2x^2-14x+20 gt 0`
or `x^2- 7 x + 10 gt 0 `
`rArr x gt 5 or x lt 2`
From (1) and (2),`5 lt x le 8 rArr x = 6,7,8`
Promotional Banner

Topper's Solved these Questions

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.4|11 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.5|12 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE|Exercise Exercise 1.2|8 Videos

  • SEQUENCE AND SERIES

    CENGAGE|Exercise Question Bank|1 Videos

  • SETS AND RELATIONS

    CENGAGE|Exercise Question Bank|3 Videos

Similar Questions

Explore conceptually related problems

The number of integral values of x satisfying the equation |x-|x-4||=4 is

The number of integral value(s) of a so that the graph of y=16 x^(2)+8(a+5) x-7 a-5 is always above the x -axis is

The number of integral values of b, for which the equation x^(2)+bx-16=0 has integral roots, is

The greatest integral value of a such that sqrt( 9 - a^2 + 2x - x^2) >= sqrt(16 - x^2) for at least one positive value of x is (a) 3 (b) 4 (c) 6 (d) 7

Integrate the functions 1/(sqrt(x^(2)+4x+10))

Integrate the function (x+2)/(sqrt(x^(2)-1))

Integrate the functions 1/(sqrt(4x-x^(2)))

Integrate the function (x-1)/(sqrt(x^(2)-1))

Integrate the functions (4x+2)sqrt(x^(2)+x+1)

Integrate the function 1/(sqrt(x^(2)+2x+2))