If x^2 + y^2 = 7xy, show that x^2/y^2 + y^2/x^2 = 47 fast pls.fastest gets brainliest if correct answer..
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If x^2 + y^2 = 7xy, show that x^2/y^2 + y^2/x^2 = 47 fast pls.fastest gets brainliest if correct answer..
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[tex] Given \: x^{2} + y^{2} = 7xy \: --(1)[/tex]
/* On squaring both sides of the equation, we get */
[tex] (x^{2} + y^{2})^{2} = (7xy)^{2} [/tex]
[tex] \implies (x^{2})^{2} + (y^{2})^{2} + 2x^{2}y^{2} = 49x^{2}y^{2} [/tex]
[tex] \boxed { \pink{ \because (a+b)^{2} = a^{2}+b^{2}+2ab }}[/tex]
[tex] \implies x^{4} + y^{4} = 49x^{2}y^{2} - 2x^{2}y^{2} [/tex]
[tex] \implies x^{4} + y^{4} = 47x^{2}y^{2} [/tex]
/* Dividing each term by x²y² , we get */
[tex] \implies \frac{x^{4}}{x^{2}y^{2}} + \frac{y^{4} }{x^{2}y^{2}}= \frac{47x^{2}y^{2} }{x^{2}y^{2}} [/tex]
[tex] \blue{\implies \frac{x^{2}}{y^{2}} + \frac{y^{2} }{x^{2}}= 47} [/tex]
Hence Proved
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