If the sum of two consecutive odd natural number is 8 and their product is 15 Find the number

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Year 10 Interactive Maths - Second Edition If x is any number, then x and x + 1 are consecutive numbers. E.g. 14 and 15 are consecutive numbers, as are 21 and 22. If the sum of two consecutive numbers is 159, find the numbers. Solution: Check: 79 + 80 = 159 Consecutive Even Numbers If x is any even number, then x and x + 2 are consecutive even numbers. E.g. 8 and 10 are consecutive even numbers, as are 24 and 26. Example 19 If the sum of two consecutive even numbers is 194, find the numbers. Solution: Check: 96 + 98 = 194 Consecutive Odd Numbers If x is any odd number, then x and x + 2 are consecutive odd numbers. E.g.  7 and 9 are consecutive odd numbers, as are 31 and 33. Example 20 If the sum of two consecutive odd numbers is 228, find the numbers. Solution: Check: 113 + 115 = 228

The sum of two natural numbers is 8 and their product is 15., Find the numbers. 

Let the required natural numbers be x and `(8-x)` 

It is given that the product of the two numbers is 15 

∴ `x(8-x)=15` 

⇒` 8x-x^2=15` 

⇒`x^2-8x+15=0` 

⇒`x^2-5x-3x+15=0` 

⇒`x(x-5)-3(x-5)=0` 

⇒`(x-5)(x-3)` 

⇒`x-5=0  or  x-3=0` 

⇒`x=5  or  x=3` 

Hence, the required numbers are 3 and 5.

Concept: Quadratic Equations Examples and Solutions

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