Sat Math problem in BB

<p>This problem is from practice test 2, section 2, number 19:
The square of x is equal to 4 times the square of y. If x is 1 more than twice y, what is the value of x?
A)-4
B)-1/2
C)-1/4
D)1/4
E)1/2
The answer is E. </p>

<p>Please tell me how you derived your answer. I really appreciate the help.</p>

<p>x^2 = 4y^2 </p>

<p>Substitute: </p>

<p>(2y+1)^2 = 4y^2 </p>

<p>Expand:</p>

<p>4y^2 + 4y + 1 = 4y^2 </p>

<p>4y = -1</p>

<p>y = -1/4</p>

<p>Substitute:</p>

<p>x^2 = 4(-1/4)^2
x^2 = 4(1/16)
x^2 = 1/4
x = 1/2</p>

<p>The reason x can't be -1/2 is because x has to be 1 more than twice y. </p>

<p>2(-1/4) + 1 = 1/2</p>

<p>x^2=4y^2
x=1 + 2y</p>

<p>Find x.</p>

<p>(1 + 2y)^2=4y^2
4y^2 + 4y + 1 = 4y^2
4y + 1 = 0
y = -1/4
x = 2(-1/4) + 1
x = 1/2</p>

<p>[E]</p>