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**FailInMaths** Question:

The subtraction of two positive numbers is $\displaystyle 4$. When the two numbers are multiplied together, the resulting value is $\displaystyle 21$. By using algebraic method, find the value of the smallest number

My workings:

let $\displaystyle x$ be the smallest number

let $\displaystyle x+4$ be the bigger number

$\displaystyle (x+4)-x=4$

$\displaystyle (x+4)$ x$\displaystyle x=21$

$\displaystyle x+4=4+x$

$\displaystyle (x^2+4x)/4 = 21/4$

$\displaystyle 4(x^2+4x)=84$

$\displaystyle 4x^2+16x=84$

$\displaystyle 4x^2+16x-84=0$

$\displaystyle (x+7)$ or $\displaystyle (4x-12)$

$\displaystyle x+7=0$ or $\displaystyle 4x-12=0$

$\displaystyle x=-7$ (N.A.) or $\displaystyle 4x-12=0$

Therefore, $\displaystyle x=3$

Am I right?

Thanks