The product of two consecutive odd numbers is 143. Find the numbers. | Quadratic Equation | SciPiPupil

Question: The product of two consecutive odd numbers is 143. Find the numbers.

Solution:

According to the question,

Condition I,

Two numbers are consecutive odd numbers.

Let one of the number be x then the other is (x+2).

Condition II,

Product of such two number is 143.

$or, x(x+2) = 143$

$or, x^2 +2x = 143$

$or, x^2 +2x -143 = 0$

$or, x^2 +(13-11)x -143 = 0$

$or, x^2 +13x -11x -143 = 0$

$or, x(x +13) -11(x +13) = 0$

$or, (x -11)(x +13) = 0$

Either,

$x -11 = 0$

$\therefore x = 11$

Or,

$x +13 = 0$

$\therefore x = -13$

Taking positive value of x = 11.

When one of the odd number is x = 11, then the other number is (11+2) = 13.

Hence, the required two numbers are 11 and 13 respectively.

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