Evaluate the expression

Algebra Level 1

If x = 102 − 10 x = \sqrt{102} - 10 , what is the value of x 2 1 − 10 x \frac {x^2} {1-10x} ?


The answer is 2.

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Arron Kau by Arron Kau

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6 solutions

Hassan Chug
Nov 7, 2013

Substitute x = 102 − 10 x = \sqrt{102} - 10 into x 2 1 − 10 x \frac{x^2}{1 - 10x}

⟹ ( 102 − 10 ) 2 1 − 10 ( 102 − 10 ) \implies \frac{(\sqrt{102} - 10)^2}{1 - 10(\sqrt{102} - 10)}

⟹ 102 − 20 102 + 100 1 − 10 102 + 100 \implies \frac{102 - 20\sqrt{102} + 100}{1 - 10\sqrt{102} + 100}

⟹ 202 − 20 102 101 − 10 102 \implies \frac{202 - 20\sqrt{102}}{101 - 10\sqrt{102}}

⟹ 2 ( 101 − 10 102 ) 101 − 10 102 \implies \frac{2(101 - 10\sqrt{102})}{101 - 10\sqrt{102}}

⟹ 2 \implies 2

30 Helpful 0 Interesting 0 Brilliant 0 Confused

nice solution

kasimayan mayan - 7 years, 7 months ago

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good

Syed Rehman - 7 years, 7 months ago

It was great! Thank you. :)

Nanelle Ilano - 7 years, 7 months ago

good....i like..it

Himanshu Verma - 7 years, 7 months ago

nice!

Anselmo Francia - 7 years, 7 months ago

great solution

Luis Talero - 7 years, 7 months ago

wow the thing i did is because theirs a square i cancelled the square root haha silly me

Vongola Decimo - 7 years, 7 months ago

nice

Jc Marcos - 7 years, 7 months ago

wow ! you're awesome !

Iswilma Emma - 7 years, 7 months ago

nice solution

Jaswant Singh - 7 years, 7 months ago

Given is x=\sqrt{102} - 10 Rearrange it as folowed x+10=\sqrt{102}

Squaring both sides x^2 + 2(10)(x) + 100 = 102

x^2 + 20x = 102-100 x^2 + 20x = 2

So

x^2 = 2 - 20x or x^2 = 2(1 - 10x)

Now substitute the value of x^2 in the fraction. frac {x^2}{1 - 10x}

= frac { 2(1 - 10x)}{1 - 10x} = 2

JD Rox - 7 years, 7 months ago

good

Sk Buriro - 7 years, 7 months ago

i was just solving it bt i lost it damn

radha hati - 7 years, 7 months ago
Jericho Cabrera
Nov 9, 2013

x = (sqrt(102)-10)^2/(1-10(sqrt(102)-10)) note: sqrt(102) = 10.09950494

therefore, x = 2

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Christian Cortez
Nov 9, 2013

square root of 102 - 10 squared = 102-100 so the answer will be 2
1-10 (square root of 102 - 10)
multiply the number 10 .. 10x10 = 100.. then solve the close parenthesis (102-100) = 2

2 over 1-2 = 2 over 1 then i solve it 2/1 is 2

sorry for my solution .. i dont know how to explain but im so interested for solving this kind of problem.. xD hope u understand i love math :D

0 Helpful 0 Interesting 0 Brilliant 0 Confused

x^2 / (1-10x) = (V102 - 10)^2 / [1-10(V102 - 10)] = 202 - 20V102 / 101 - 10V102 = 2

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Saish Talauliker
Nov 9, 2013

rearanging we get (x+10)^2=102 x^2+20x+100=102 x^2=2-20x x^2=2(1-10x)

hence given exprsn =2

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Arben Osmani
Nov 8, 2013

x=sqrt(102)-10;

((sqrt(102)-10)^3)/(1-10(sqrt(102)-10)) =(102-20 sqrt(102)+100)/(1-10sqrt(102)+100) =(202-20 sqrt(102))/(101-10sqrt(102)) =(2(101-10sqrt(102))/(101-10sqrt(102)) =2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

nice...

Uttam Vaghasiya - 7 years, 7 months ago

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