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$\$.MathematicsRS AgarwalStandard X

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