Question : If $(a^3+b^3+c^3-3 a b c)=405$ and $(a-b)^2+(b-c)^2+(c-a)^2=54$, find the value of $(a + b + c)$.
Option 1: 15
Option 2: 45
Option 3: 9
Option 4: 27
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: 15
Solution : $(a-b)^2+(b-c)^2+(c-a)^2=54$ ⇒ $2(a^2+b^2+c^2-ab-bc-ac)=54$ ⇒ $(a^2+b^2+c^2-ab-bc-ac)=27$ Also, we know that $(a^3+b^3+c^3-3 a b c) = (a+b+c)(a^2+b^2+c^2-ab-bc-ac)$ Substituting the values, ⇒ $405 = 27×(a+b+c)$ ⇒ $a+b+c = 15$ Hence, the correct answer is 15.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If $(a + b + c) = 13$ and $(ab + bc + ca) = 54$, find the value of $\left(a^2+b^2+c^2\right)$.
Question : If $(a+b+c)=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3+c^3-3 abc$.
Question : Directions: If A denotes +, B denotes –, C denotes × and D denotes ÷, then which of the following equations is true?
Question : If $\frac{1}{a}(a^2+1)=3$, then the value of $\frac{a^6+1}{a^3}$ is:
Question : If $a+b-c=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3-c^3+3abc$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile