Home
Class 12
MATHS
The number of integral values of x satis...

The number of integral values of `x` satisfying `sqrt((-x^(2)+10x-16))ltx-2` is

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 ENGLISH|Exercise Concept Application Exercise 1.4|11 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 1.5|12 Videos

  • SET THEORY AND REAL NUMBER SYSTEM

    CENGAGE ENGLISH|Exercise Concept Application Exercise 1.2|8 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Find the number of integal values of x satisfying sqrt(-x^2+10x-16) lt x -2

Find the number of integal values of x satisfying sqrt(-x^2+10x-16) lt x -2

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

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

The number of integral values of x satisfying the inequality (3/4)^(6x+10-x^2)<(27)/(64) is _____

Number of integral values of 'x' satisfying |x+4|+|x-4|=8 is :-

If number of integral values of x satisfying the inequality ((x)/(100))^(7logx-log^(2)x-6)ge10^(12) are alpha then

Number of integral values of x satisfying function f(x)=log(x-1)+log(3-x)

The number of integral value(s) of x satisfying the equation |x^4 .3^(|x-2|). 5^(x-1)|=-x^4 .3^(|x-2|). 5^(x-1) is

Find the smallest integral value of x satisfying (x-2)^(x^2-6x+8))>1