Question

(i) 3 minus 2 square​

Answer 1

Answer:

minus one is the answer when 2 square is subtracted from 3

Answer 2

Answer:

The\:value \: of \: \\a^{2}-\frac{1}{a^{2}}\\=-24\sqrt{2}

step by step explanation

Given \: a = 3-2\sqrt{2}--(1)

i)\frac{1}{a}=\frac{1}{3-2\sqrt{2}}\\=\frac{(3+2\sqrt{2})}{(3-2\sqrt{2})(3+2\sqrt{2})}\\=\frac{(3+2\sqrt{2})}{3^{2}-(2\sqrt{2})^{2}}\\=\frac{(3+2\sqrt{2})}{9-8}\\=3+2\sqrt{2}---(2)

ii) a+\frac{1}{a}\\=3-2\sqrt{2}+3+2\sqrt{2}\\=6---(3)

iii) a-\frac{1}{a}\\=3-2\sqrt{2}-(3+2\sqrt{2})\\=3-2\sqrt{2}-3-2\sqrt{2}\\=-4\sqrt{2}---(4)

Now,\\a^{2}-\frac{1}{a^{2}}\\=\left(a+\frac{1}{a}\right)\left(a-\frac{1}{a}\right)\\=6\times (-4\sqrt{2})\\=-24\sqrt{2}

Therefore,

The\:value \: of \: \\a^{2}-\frac{1}{a^{2}}\\=-24\sqrt{2}