sqrt x +1= sqrt x +7= solve and check answer

Question

sqrt  x +1= sqrt x +7= solve and check answer

geerky42 · Answer

try to square both sides.

xapproachesinfinity · Answer

Yes square both side to get x+1=x+7
and solve

xapproachesinfinity · Answer

that if square cover x+1 and x+7

xapproachesinfinity · Answer

that is*

aum · Answer

You have to make it clear where the square root stops with x + 1. Are both x and +1 within the square root or just x? Same thing with x + 7. Are both x and +7 within the square root or just x?

aum · Answer

Use parenthesis to make it clear.

anonymous · Answer

x+1 within sqrt = x+7 within sqrt

aum · Answer

$$
\sqrt{x+1} = \sqrt{x+7}~~ ?
$$

anonymous · Answer

yes exactly

aum · Answer

There is NO solution to that.

aum · Answer

There is no value of x to which you can add a 1 OR a 7, take the square root and end up with the same value.

anonymous · Answer

there is a very short sqrt over x+1 then a long sqrt over x+7

aum · Answer

$$
\sqrt{x} + 1 = \sqrt{x+7} ~~~?  \
$$Don't say exactly unless you are sure.

anonymous · Answer

yes I am looking at the paper.

aum · Answer

You can post a screenshot of the question if you can.

anonymous · Answer

don't know how but you have it as written like it is on the paper.  I only have a few minutes to answer the next few question.

aum · Answer

$$
\sqrt{x} + 1 = \sqrt{x+7} \
\text{Square both sides:} \
x + 1 + 2\sqrt{x} = x + 7 \
2\sqrt{x} = 6 \
\text{Square both sides:} \
4x = 36 \
x = 9
$$

aum · Answer

substitute back and make sure x = 9 works.

anonymous · Answer

thank you Aum.  I have one more for you.  Long sq rt Y-9=short sqrt Y-1

aum · Answer

Use the same method shown above.