Question : If $a+b+c=5$ and $a^2+b^2+c^2=15$, then find the value of $a^3+b^3+c^3-3 a b c-27$.
Option 1: 23
Option 2: 27
Option 3: 25
Option 4: 21
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 23
Solution : Given: $a+b+c=5$ and $a^2+b^2+c^2=15$ We know, $(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$ $⇒(5)^2=15+2(ab+bc+ca)$ $⇒2(ab+bc+ca)=10$ $⇒ab+bc+ca=5$ -------------------------------------------(1) Also, $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ $⇒a^3+b^3+c^3-3abc=5(15-(ab+bc+ca))$ $⇒a^3+b^3+c^3-3abc=5(15-5)$ $⇒a^3+b^3+c^3-3abc=50$ Now, $a^3+b^3+c^3-3abc-27=50-27=23$ Hence, the correct answer is 23.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : If $a: b=3: 7$, then $(2 a+3 b):(3 a+2 b)$ is:
Question : If $a+b+c=15$ and $a b+b c+c a=22$, then find the value of $a^2+b^2+c^2$.
Question : If (a + b + c) = 7 and ab + bc + ca = 12, find the value of a2 + b2 + c2.
Question : If $a+b=3$ and $a b=2$, then what is the value of $2 a^3+2 b^3$?
Question : If $a+b=10$ and $a^2+b^2=58$, find the value of $ab$
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile