Question : If $a^{2}+13b^{2}+c^{2}-4ab-6bc=0$, then $a:b:c$ is:
Option 1: $1:2:3$
Option 2: $2:3:1$
Option 3: $2:1:3$
Option 4: $1:3:2$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $2:1:3$
Solution : Given: $a^{2} + 13b^{2} + c^{2} - 4ab - 6bc = 0$ ⇒ $a^{2} - 4ab + 4b^{2} + 9b^{2} + c^{2} - 6bc = 0$ ⇒ $a^{2} - 4ab + 4b^{2} + c^{2} - 6bc + 9b^{2} = 0$ ⇒ $(a - 2b)^{2} + (c - 3b)^{2} = 0$ ⇒ $a - 2b = 0$ and $c - 3b = 0$ [if the sum of the squares of two numbers is zero then each of the numbers will also be zero] ⇒ $a = 2b$ and $c = 3b$ ⇒$a:b = 2: 1$ and $b : c = 1: 3$ $\therefore a:b:c = 2:1:3$ Hence, the correct answer is $a:b:c = 2:1:3$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : If $a+b+c = 0$, then the value of $\small \frac{1}{(a+b)(b+c)}+\frac{1}{(b+c)(c+a)}+\frac{1}{(c+a)(a+b)}$ is:
Question : If $a, b, c$ are real numbers and $a^{2}+b^{2}+c^{2}=2(a-b-c)-3,$ then the value of $a+b+c$ is:
Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?
Question : If $\frac{a^2}{b+c}=\frac{b^2}{c+a}=\frac{c^2}{a+b}=1$, then find the value of $\frac{2}{1+a}+\frac{2}{1+b}+\frac{2}{1+c}$.
Question : If $\frac{a^2+b^2}{c^2}=\frac{b^2+c^2}{a^2}=\frac{c^2+a^2}{b^2}=\frac{1}{k}$, $(k\neq 0)$, then $k$=?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile