Question

$2x+\frac2x=3$ হলে, $x^2+\frac1{x^2}$ এর মান কত?

Answer 1

দেওয়া আছে,
$2x+\frac2x=3$

বা, $2\left(x+\frac{1}{x}\right)=3$

বা, $\left(x+\frac{1}{x}\right)=\frac32$

বা, $\left(x+\frac{1}{x}\right)^2=\left(\frac32\right)^2$

বা, $x^2+2\cdot x \cdot \frac1x +\frac{1}{x^2}=\frac94$

বা, $x^2+2+\frac{1}{x^2}=\frac94$

বা, $x^2+\frac{1}{x^2}=\frac94-2$

বা, $x^2+\frac{1}{x^2}=\frac{9-8}{4}$

$\therefore x^2+\frac{1}{x^2}=\frac14$ [Answer]

Comments

Rules Applied:

• $(a+b)^2=a^2+2ab+b^2$