Question : If $x^4+x^2 y^2+y^4=21$ and $x^2+xy+y^2=3$, then what is the value of $4xy $?
Option 1: –8
Option 2: 4
Option 3: –4
Option 4: 12
Correct Answer: –8
Solution : We have, $x^4+x^2 y^2+y^4=21$ and, $x^2+xy+y^2=3$ -----------------(i) Use the identity, $x^4+x^2 y^2+y^4=(x^2-x y+y^2)(x^2+x y+y^2)$ $⇒21=3(x^2-x y+y^2)$ $⇒x^2-x y+y^2=7$ ---------------------(ii) From (i) and (ii), $⇒2xy=-4$ $⇒4xy=-8$ Hence, the correct answer is –8.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?
Question : If $x^2+8 y^2+12 y-4 x y+9=0$, then the value of $(7 x+8 y)$ is:
Question : If $x$ and $y$ are real numbers, then the least possible value of $4 (x -2)^2+ (y-3)^2-2 (x-3)^2$ is:
Question : If $x + y + z =1$, $xy + yz + zx = - 26$, and $x^3+y^3+z^3 = 151$. then what will be the value of $xyz$?
Question : If $x^2+8 y^2-12 y-4 x y+9=0$, then the value of $(7x-8y)$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile