The number of positive integral values of x satisfying x2-7 x-12-x2-13 x-22- 1- is

X^2 7x+12x^2 13x+22≤ 1 ⇒ nbsp;x^2 7x+12x^2 13x+22 1≤ 0 ⇒6x 10x^2 13x+22≤ 0 ⇒2(3x 5)(x 11)(x 2)≤ 0 By wavy curve method, x ∈( ∞, 5 3]∪(2, 11) So, the ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Graph of Quadratic Expression

The number of...

Question

The number of positive integral values of $x$ satisfying $\frac{x^{2} - 7 x + 12}{x^{2} - 13 x + 22} \leq 1$ , is

Open in App

Solution

$\frac{x^{2} - 7 x + 12}{x^{2} - 13 x + 22} \leq 1 \Rightarrow \frac{x^{2} - 7 x + 12}{x^{2} - 13 x + 22} - 1 \leq 0 \Rightarrow \frac{6 x - 10}{x^{2} - 13 x + 22} \leq 0 \Rightarrow \frac{2 (3 x - 5)}{(x - 11) (x - 2)} \leq 0$

By wavy curve method,
$x \in (- \infty, \frac{5}{3}] \cup (2, 11)$
So, the positive integral values of $x$ are $1, 3, 4, 5, 6, 7, 8, 9, 10$
Hence, the required number of values of $x$ is $9$ .

Suggest Corrections

Similar questions

Q. Least integral value of

x

satisfying the inequation

(x^{2} + 1) < {(x + 2)}^{2} < 2 x^{2} + 4 x - 12

Q. Least integral value of

x

satisfying the in equation

(x^{2} + 1) < {(x + 2)}^{2} < 2 x^{2} + 4 x - 12

Q. The number of integral values of x satisfying

\sqrt{- x^{2} + 10 x - 16} < x - 2

Q. The number of integral values of

x

satisfying

\sqrt{- x^{2} + 10 x - 16} < x - 2

Q. Number of integral values of

x

satisfying

| x^{2} - 5 x + 4 | = 2

Join BYJU'S Learning Program

The number of positive integral values of x satisfying x2−7x+12x2−13x+22≤1, is

x2−7x+12x2−13x+22≤1⇒x2−7x+12x2−13x+22−1≤0⇒6x−10x2−13x+22≤0⇒2(3x−5)(x−11)(x−2)≤0 By wavy curve method, x∈(−∞,53]∪(2,11) So, the positive integral values of x are 1,3,4,5,6,7,8,9,10 Hence, the required number of values of x is 9.

The number of positive integral values of $x$ satisfying $\frac{x^{2} - 7 x + 12}{x^{2} - 13 x + 22} \leq 1$ , is