Question

X^2-10x-11=0 Determine which equation has the same solutions as the given equation.

Answer 1

Rather than looking for the solutions of each equation, let's see which of the options actually is the same equation as the one above. At that point, if we prove that two equations are the same, they necessarily have the same solutions.

We can see that the options feature either $(x-5)^2$ or $(x-10)^2$. If we expand them, we have

$(x-5)^2 = x^2-10x+25,\quad (x-10)^2 = x^2-20x+100$

Since the original equation has the $-10x$ term, the answer is either option a) or c). To find which of the two is correct, we consider the additional terms. Option a becomes, if you move 36 to the left hand side,

$x^2-10x+25 = 36 \iff x^2-10x-11 = 0$

while option c becomes, if you move 21 to the other side,

$x^2-10x+25 = 21 \iff x^2-10x+4 = 0$

So, option a, when expanded and rearranged, is exactly the same equation as the one above, and as such, has the same solutions.

Answer 2

Answer:A

Step-by-step explanation: