Advertisements
Advertisements
Question
Find two consecutive even natural numbers such that the sum of their squares is 340.
Advertisements
Solution
Let first even natural number = 2x
Then second number = 2x + 2
According to the condition,
(2x)2 + (2x + 2)2 = 340
4x2 + 4x + 8x + 4 = 340
⇒ 8x2 + 8x + 4 - 340 = 0
⇒ 8x2 + 8x - 336 = 0
⇒ x2 + x - 42 = 0 ...(Dividing by 8)
⇒ x2 + 7x - 6x - 42 = 0
⇒ x(x + 7) -6(x + 7) = 0
⇒ (x + 7)(x - 6) = 0
EIther x + 7 = 0,
then x = -7
or
x - 6 = 0,
then x = 6
∴ First even natural number = 2x
= 2 x 6
= 12
and second
= 12 + 2
= 14
∴ Numbers are 12, 14.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
Solve each of the following equations by factorization:
`x+1/x=2.5`
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Solve the following equation: 4x2 - 13x - 12 = 0
Solve the following equation : x2 + 2ab = (2a + b)x
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
(x – 3) (x + 5) = 0 gives x equal to ______.
