Question

$x^2+y^2 +z^2 = 2$, $xy + yz + zx = 1$ হলে, $(x + 2y)^2 + (y + 2z)^2 + (z + 2x)^2$ এর মান কত?

Visit to study 46th BCS 200 MCQ & Solution

Answer 1

$(x + 2y)^2 + (y + 2z)^2 + (z + 2x)^2$

$=\left(x^2 + 2 \cdot x \cdot 2y + (2y)^2\right) + $$\left(y^2 + 2 \cdot y \cdot 2z + (2z)^2\right) + $$\left(z^2 + 2 \cdot z \cdot 2x + (2x)^2\right)$

$=\left(x^2 + 4xy + 4y^2\right) + $$\left(y^2+ 4yz + 4z^2\right) + $$\left(z^2 + 4xz + 4x^2\right)$

$=x^2 + 4xy + 4y^2 + $$y^2+ 4yz + 4z^2 + $$z^2 + 4xz + 4x^2$

$=5x^2 + 5y^2 + 5z^2 + 4xy + 4yz + 4xz$

$=5(x^2 + y^2 + z^2) + 4(xy + yz + xz)$

$=5 \times 2 + 4 \times 1$ [ মান বসিয়ে ]

$=10 + 4$

$=14$