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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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