Question
Determine. if 3 is a root of the equation given below:
$\sqrt{\text{x}^2-4\text{x}+3}+\sqrt{\text{x}^2-9}=\sqrt{4\text{x}^2-14\text{x}+16}$
$\sqrt{\text{x}^2-4\text{x}+3}+\sqrt{\text{x}^2-9}=\sqrt{4\text{x}^2-14\text{x}+16}$
✓
Answer
$\sqrt{\text{x}^2-4\text{x}+3}+\sqrt{\text{x}^2-9}=\sqrt{4\text{x}^2-14\text{x}+16}$
If x = 3, then
L.H.S. $\sqrt{\text{x}^2-4\text{x}+3}+\sqrt{\text{x}^2-9}$
$=\sqrt{(3)^2-4\times3+3}+\sqrt{(3)^2-9}$
$=\sqrt{9-12+3}+\sqrt{9-9}$
$=\sqrt{0}+\sqrt{0}$
$=0$
R.H.S. $=\sqrt{4\text{x}^2-14\text{x}+16}$
$=\sqrt{4(3)^2-14\times3+16}$
$=\sqrt{4\times9-42+16}$
$=\sqrt{36+16-42}$
$=\sqrt{52-42}$
$=\sqrt{10}$
$\because$ L.H.S. $\neq$ R.H.S.
If x = 3, then
L.H.S. $\sqrt{\text{x}^2-4\text{x}+3}+\sqrt{\text{x}^2-9}$
$=\sqrt{(3)^2-4\times3+3}+\sqrt{(3)^2-9}$
$=\sqrt{9-12+3}+\sqrt{9-9}$
$=\sqrt{0}+\sqrt{0}$
$=0$
R.H.S. $=\sqrt{4\text{x}^2-14\text{x}+16}$
$=\sqrt{4(3)^2-14\times3+16}$
$=\sqrt{4\times9-42+16}$
$=\sqrt{36+16-42}$
$=\sqrt{52-42}$
$=\sqrt{10}$
$\because$ L.H.S. $\neq$ R.H.S.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A plane left $30$ minutes late than its scheduled time and in order to reach the destination $1500 \ km $ away in time, it had to increase its speed by $100 \ km/h$ from the usual speed. Find its usual speed.
→In the given figure, a circle inscribed in a triangle ABC touches the sides AB, BC and CA at points D, E and F respectively. If AB = 14cm, BC = 8cm and CA = 12cm. Find the lengths AD, BE and CF.
Solve the pair of linear equations $3x + 4y = 10$ and $2x – 2y = 2$ by elimination and substitution method.
→If the mean of the following data is 18.75. Find the value of p.
| x | 10 | 15 | P | 25 | 30 |
| f | 5 | 10 | 7 | 8 | 2 |
A game consists of tossing a coin three times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Find $n$ if the given value of $x$ is the $n^{\text {th }}$ term of the given A.P.
$-1,-3,-5,-7, \ldots \ldots ; x=-151$
→$-1,-3,-5,-7, \ldots \ldots ; x=-151$
Which term of the AP 5, 15, 25, .... will be 130 more than its $31^{st}$ term?
→Prove that $\sqrt { 3 }$ is irrational.
→In the figure below, a decorative block, made up of two solids $-$ a cube and a hemi $-$ sphere? The base of the block is a cube of side $6 \ cm$ and the hemisphere fixed on the top has a diameter of $3.5 \ cm$ . Find the total surface area of the block. $\text { (use } \left.\pi=\frac{22}{7}\right)$
→Reena has pend and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, the number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.