Question:
If
\[
\frac{x+a}{b+c}+\frac{x+b}{c+a}+\frac{x+c}{a+b}=3
\]
and
\[
a+b+c=5,
\]
then \(x=\)
If
\[
\frac{x+a}{b+c}+\frac{x+b}{c+a}+\frac{x+c}{a+b}=3
\]
and
\[
a+b+c=5,
\]
then \(x=\)
Show Hint
Use the given sum relation to rewrite variables and simplify the expression quickly.
Updated On: Jul 15, 2026
- \(-2\)
- \(-3\)
- \(-4\)
- \(-5\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Given:
\[
a+b+c=5
\]
So:
\[
a=5-(b+c),\; b=5-(c+a),\; c=5-(a+b)
\]
Substitute:
\[
\frac{x+5-(b+c)}{b+c}+\frac{x+5-(c+a)}{c+a}+\frac{x+5-(a+b)}{a+b}=3
\]
\[
\frac{x+5}{b+c}-1+\frac{x+5}{c+a}-1+\frac{x+5}{a+b}-1=3
\]
\[
(x+5)\left(\frac1{b+c}+\frac1{c+a}+\frac1{a+b}\right)=6
\]
Thus the only possible value satisfying the identity is:
\[
x=-5
\]
Hence:
\[
\boxed{-5}
\]
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Algebra Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
- If \[ \frac{7}{\sqrt3+\sqrt{10}} + \frac{8}{\sqrt3+\sqrt7} + \frac{9}{\sqrt7+\sqrt{10}} = p\sqrt3+q\sqrt7+r\sqrt{10}, \] then \(p^2+q^2+r^{-2}\) equals:
- The sum of a rational number \(x\) and its reciprocal is \(\frac{113}{56}\). If \(x=\frac{m}{n}\), where \(\gcd(m,n)=1\), then \(m^2+n^2=\ ?\)
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions