Question

if x/y + y/X =3 let's find the value of X2/y2+y2/x2​

Answer 1

Answer:

$\frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}= 7$

Step-by-step explanation:

$Given\: \frac{x}{y}+\frac{y}{x} = 3\: ---(1)$

/* On Squaring both sides of the equation, we get

$\left(\frac{x}{y}+\frac{y}{x}\right)^{2} = 3^{2}$

$\implies \left(\frac{x}{y}\right)^{2}+\left(\frac{y}{x}\right)^{2}+2\times \left(\frac{x}{y}\right)\times \left(\frac{y}{x}\right)= 9$

$\implies \frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}+ 2 = 9$

$\implies \frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}= 9-2$

$\implies \frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}= 7$

Therefore,

$\frac{x^{2}}{y^{2}}+\frac{y^{2}}{x^{2}}= 7$

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