Solving for $X$: Find $X$ When $X=Y^2$

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In summary, the process for solving for X when X equals Y squared is to take the square root of both sides of the equation and plug in the value of Y to find the corresponding values for X. To check if your solution for X is correct, you can plug it back into the original equation. Yes, you can solve for X if Y is a negative number, but you must remember to include both positive and negative square root solutions for X. The only restriction is that Y cannot be 0. This equation can be used to solve for X in any problem where X is equal to the square of another variable. It is commonly used in math and science, particularly in problems involving quadratic equations.
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Albert1
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$X=\overline{abcdef}$ is a 6-digit number,

$Y=\overline{def}$ is a 3-digit number,

if $X=Y^2$ find $X$
 
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  • #2
Albert said:
$X=\overline{abcdef}$ is a 6-digit number,

$Y=\overline{def}$ is a 3-digit number,

if $X=Y^2$ find $X$

let $X = 1000m + Y$
we have $X = Y^2$ or $Y^2-Y= 1000m$ or $Y(Y-1) = 1000m = (125a)(8b)$ where $m = ab$
now $Y,Y-1$ are co-primes so one of them has to be 125a and another 8b and a and b are coprimes or one of them is 1
a has to be odd ( else 125 cannot be coprime to 8b) and < 8 as $Y < 1000$
so we get
$Y=125a, Y-1 = 8b$ trying a = 1,3,5,7 we get $Y= 625, Y-1 = 624 = 8 * 78$
or
$Y=8b, Y-1 = 125a$ we get $Y = 376$
so there are 2 values of X $ 376^2 = 141376$ and $625^2=390625$
 

FAQ: Solving for $X$: Find $X$ When $X=Y^2$

What is the process for solving for X when X equals Y squared?

The process for solving for X when X equals Y squared is to take the square root of both sides of the equation. This will give you two possible solutions for X, as there are both positive and negative square roots. You can then plug in the value of Y to find the corresponding values for X.

How do I know if my solution for X is correct?

To check if your solution for X is correct, you can plug the value of X back into the original equation and see if it satisfies the equation. If it does, then your solution is correct. If not, you may need to double check your calculations.

Can I solve for X if Y is a negative number?

Yes, you can still solve for X if Y is a negative number. The process is the same, but you will have to remember to include both the positive and negative square root solutions for X.

Are there any restrictions to solving for X when X=Y^2?

The only restriction to solving for X when X equals Y squared is that Y cannot be equal to 0. This is because you cannot take the square root of 0, so there would be no solution for X.

Can I use this equation to solve for X in any type of problem?

Yes, you can use this equation to solve for X in any problem where X is equal to the square of another variable. This type of equation is commonly used in math and science, especially in problems involving quadratic equations.

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