Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:
Option 1: 6
Option 2: 9
Option 3: 0
Option 4: 1
Latest: SSC CGL Tier 1 Result 2024 Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: 0
Solution : Given: $x+y+z=9$ Solution: Let $(x–4) = a, (y−2) = b, (z−3) = c$ So, this equation stands to $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ = $a^3+b^3+c^3–3abc$ Also, We know that $a^3+b^3+c^3–3abc$ = $(a+b+c)(a^2+b^2+c^2–bc–ab–ac) $. So, $a+b+c = x−4+y−2+z−3$ ⇒ $a+b+c = x+y+z−9$ ⇒ $a+b+c = 9−9$ ⇒ $a+b+c = 0$ So, $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)=0$ Hence, the correct answer is 0.
Candidates can download this ebook to know all about SSC CGL.
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?
Question : $\text { If } x^2+y^2+z^2=x y+y z+z x \text { and } x=1 \text {, then find the value of } \frac{10 x^4+5 y^4+7 z^4}{13 x^2 y^2+6 y^2 z^2+3 z^2 x^2}$.
Question : If $\frac{(x+y)}{z}=2$, then what is the value of $[\frac{y}{(y-z)}+\frac{x}{(x-z)}]?$
Question : If $(x-5)^2+(y-2)^2+(z-9)^2=0$, then value of $(x+y-z)$ is:
Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{6(x-y)(y-z)(z-x)}$, where $x \neq y \neq z$, is equal to:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile