Question

Find two decimal numbers whose sum is 1 and product is 0.25. answer with steps​

Answer 1

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Answer 2

Given: Sum of two decimal numbers=1

           Product of two decimal numbers=0.25

To find The two decimal numbers

Solution: Just like we perform addition, subtraction, division, and multiplication for arithmetic and algebraic numbers, we also do the same for decimal numbers. These numbers have two parts, which is distinguished by a decimal point.

Let the required decimal numbers are a and b, then from above, we have

a+b=1  and a×b=0.25

a+b=1

⇒b=1-a  [changing side for 'a']

∴ a×b=0.25

⇒a(1-a)=0.25  [substituting the value of 'b']

⇒a-a²=0.25

⇒a²-a+0.25=0  [rearranging the above form]

⇒a²-0.5a-0.5a+0.25=0  [factorising the equation]

⇒a(a-0.5)-0.5(a-0.5)=0

⇒(a-0.5)(a-0.5)=0

⇒(a-0.5)²=0

⇒a-0.5=0  [taking squareroot on both sides]

⇒a=0.5

∴ b=1-a

⇒b=1-0.5   [substituting the value of 'a']

⇒ b=0.5

∴ a=0.5 and b=0.5

Hence the two decimal numbers are 0.5 and 0.5