Algebra 1

Algebra Level pending

Let a , b a,b and x x satisfy the system of equations below. { x = ± a a + b = x b = 2 a \begin{cases} \sqrt x = \pm a \\ a + b = x \\ b = 2a \end{cases} Which of the following options is a possible value of x + a + b x+a+b ?

18 34 99 300

J-P Coulson by J-P Coulson , 16, United Kingdom

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1 solution

J-P Coulson
Jan 10, 2021

Firstly, replace all "b's" with 2a (b=2a)

a+b=x is now 3a=x

Since the square root of x = ±a we can conclude that x must be 9

This means a = 3

Now we have to find x+a+b

This is now simple addition.

3(3)=9 (3a=x)

9+9=18

1 Helpful 0 Interesting 0 Brilliant 0 Confused

a = 3 a=3 is not the only solution to a 2 = 3 a a^2=3a ...

Chris Lewis - 5 months ago

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