Question

If y = 7-4root3 then find y^2/7y+1/7y

Answer 1

Answer:

y=4-13

Step-by-step explanation:

Answer 2

Answer:

\frac{1}{x^{2}}+\frac{1}{y^{2}}=194

Step-by-step explanation:

Given\: x=7+4\sqrt{3}\:--(1)

xy = =1\implies y =\frac{1}{x}\:--(2)

y = \frac{1}{7+4\sqrt{3}}

=\frac{7-4\sqrt{3}}{(7+4\sqrt{3})(7-4\sqrt{3})}

=\frac{7-4\sqrt{3}}{7^{2}-\left(4\sqrt{3}\right)^{2}}

=\frac{7-4\sqrt{3}}{49-48}

=7-4\sqrt{3}\: ---(3)

Now,\\\frac{1}{x^{2}}+\frac{1}{y^{2}}

=\frac{1}{\frac{1}{y^{2}}}+x^{2}

=y^{2}+x^{2}\\=(7-4\sqrt{3})^{2}+(7+4\sqrt{3})^{2}\\=2[7^{2}+(4\sqrt{3})^{2}]

/* We know the algebraic identity:

(a-b)²+(a+b)² = 2(a²+b²) */

=2(49+48)\\=2\times 97\\=194

Therefore,

\frac{1}{x^{2}}+\frac{1}{y^{2}}=194

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