Math, asked by MATHY111, 1 year ago

if a is equal to 1 minus root 2 then find the value of a minus one upon a raise to the power 3

Answers

Answered by Anant02
2

a = 1 -  \sqrt{2}   \\  {a}^{2}  = 1 + 2 - 2 \sqrt{2} = 3  -  2 \sqrt{2}   \\  {a}^{3} = (1 -  \sqrt{2})(3 - 2 \sqrt{2} ) = 3 - 3 \sqrt{2} - 2 \sqrt{2 } + 4 = 7 - 5 \sqrt{2}    \\  {a}^{4}  = 9 + 8 - 12 \sqrt{2}  = 17 - 12 \sqrt{2}  \\ a -  \frac{1}{ {a}^{3} }  =  \frac{ {a}^{4}  - 1}{ {a}^{3} }  =  \frac{17 - 12 \sqrt{2}  - 1}{7 - 5 \sqrt{2} }  \\   = \frac{16 - 12 \sqrt{2} }{7 - 5 \sqrt{2} }  =  \frac{(16 - 12 \sqrt{2} )(7 + 5 \sqrt{2}) }{(7 + 5 \sqrt{2} )(7 - 5 \sqrt{2} )}  \\  =  \frac{112 - 84 \sqrt{2} + 80 \sqrt{2} - 120 }{49 - 50}  \\  =  \frac{ - 8 - 4 \sqrt{2} }{ - 1}  = 8 + 4 \sqrt{2}
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