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Question

Find two numbers whose sum is 27 and product is 182.


Solution

Let the first number be $$x$$ then the second number will be $$27-x.$$

$x(27-x)=182$$
$$\Rightarrow 27x-{ x }^{ 2 }=182$$
$$\Rightarrow { x }^{ 2 }-27x+182=0$$
$$\Rightarrow { x }^{ 2 }-13x-14x+182=0$$
$$\Rightarrow x(x-13)-14(x-13)=0$$
$$\Rightarrow (x-14)(x-13)=0$$
$$\Rightarrow x=14,13$$

If the first number is $$14,$$ then the second number is $$13$$ and if the first number is $$13,$$ then the second number is $$14$$.

Mathematics
RS Agarwal
Standard X

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