Question : If $a + b = 24$ and $8ab = 256$, then what is the value of $3 a^2+3 b^2?$
Option 1: 1536
Option 2: 1024
Option 3: 512
Option 4: 1636
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: 1536
Solution : Given, $a + b = 24$ and $8ab = 256$ ⇒ $2ab=\frac{256}{4}=64$ We know, $(a+b)^2=a^2+b^2+2ab$ Consider $a + b = 24$ Squaring both sides, ⇒ $a^2+b^2+2ab=24^2$ ⇒ $a^2+b^2+64=576$ ⇒ $a^2+b^2=576-64$ ⇒ $a^2+b^2=512$ ⇒ $3a^2+3b^2=3\times 512$ ⇒ $3a^2+3b^2=1536$ Hence, the correct answer is 1536.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : What is the value of 512 × 3 – 25 ÷ 15 × 9?
Question : What is the value of $(a+b)^2+(a-b)^2$?
Question : If $a-b=2$ and $ab=24$, then what is the value of $a^3-b^3$?
Question : What is the value of (22 + 1)(24+1)(28 + 1)(216 + 1) .........(2128 + 1)?
Question : Directions: If 36 @ 2 = 1296 and 4 @ 4 = 256, then 9 @ 3 = ?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile