The variable question

Algebra Level 2

x 3 + x 2 9 = 0 |x-3| + \sqrt{x^{2}-9} = 0

Solve for x x .


The answer is 3.

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1 solution

x 3 a n d x 2 9 |x-3| and \sqrt{x^{2}-9} both are positive .

if sum of two positives is zero then both positives should be zero.

x 3 = 0 |x-3| = 0 which gives x =3

x 2 9 = 0 \sqrt{x^{2}-9} = 0 which gives x =3 or x=-3

So,common solution of x is 3

it can be also done by squaring both sides,but i want to depict an another method

Good method, even better then the way I solved it!

Zakir Husain - 11 months, 2 weeks ago

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Yeah exactly, I didn't observe that both are always positive. @Kriti Kamal Upvoted

Mahdi Raza - 11 months, 2 weeks ago

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@Mahdi Raza Have you solved new Pre RMO questions? (posted today)

Zakir Husain - 11 months, 2 weeks ago

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@Zakir Husain Yes, both are nice. What is k equal to 510 or 420?I am confused by the discrepancy in the solutions

Mahdi Raza - 11 months, 2 weeks ago

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@Mahdi Raza k = 420 k=420 in A Pre-RMO question! -22

Zakir Husain - 11 months, 2 weeks ago

@Mahdi Raza thanks

A Former Brilliant Member - 11 months, 2 weeks ago

I solved it the same way, but one note: zero is not positive, so the functions are not positive, they're greater than or equal to zero.

Ved Pradhan - 11 months, 2 weeks ago

@Zakir Husain thanks

A Former Brilliant Member - 11 months, 2 weeks ago

@Zakir Husain , @Mahdi Raza visit my find velocity problem

A Former Brilliant Member - 11 months, 2 weeks ago

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I have visited it

Zakir Husain - 11 months, 2 weeks ago

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@Zakir Husain in solution i have given the condition for quadration function to be equation of distance . Please check it.

A Former Brilliant Member - 11 months, 2 weeks ago

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