I need help with three homework questions.¨
First one:
$$\sqrt{3x^2-2x-15}=x+1$$ I don't know how to get the right answer. The answer is supposed to be 4. I get: $$ 3x^2-2x-15=(x+1)^2$$ $$ 3x^2-2x-15=x^2+2x+1$$ $$ 2x^2-4x-14=0$$ $$ x^2-2x-7=0$$
$$ x_1=1+\sqrt8$$ $$ x_2=1-\sqrt8$$
Second question is: $$ ln(x-7)-2ln(x-1)=-2ln5$$ where i come to this stage but don't know how to solve it $$\frac{x-7}{(x-1)^2}=\frac{1}{25}$$
the answer is supposed to be $x=11$ or $x=16$
Third question is $$9^x-4*3^x+3=0$$
I have come this far $$3^{2x}-4*3^x+3=0$$
answer is supposed to be $x=1$ or $x=0$
1) $-15 - 1 = -16$ not $-14$.
2) multiply by sides to get: $25(x -7) = (x - 1)^2$
3) $3^{2x} + 4*3^x + 3 = 0$. Let $y = 3^x$ so to get $y^2 + 4y + 3 = 0$. Easier?