Advertisements
Advertisements
Question
Find two consecutive odd integers such that the sum of their squares is 394.
Advertisements
Solution
Let first odd integer = 2x + 1
Then second odd integer = 2x + 3
According to the condition,
(2x + 1)2 + (2x + 3)2 = 394
⇒ 4x2 + 4x + 1 + 4x2 + 12x + 9 = 394
⇒ 8x2 + 16x - 394 + 10 = 0
⇒ 8x2 + 16x - 384 = 0
⇒ x2 + 2x - 48 = 0 ...(Dividing by 8)
⇒ x2 + 8x - 6x - 48 = 0
⇒ x(x + 8) -6(x + 8) = 0
⇒ (x + 8)(x - 6) = 0
EIther x + 8 = 0,
then x = -8
or
x - 6 = 0,
then x = 6
(i) If x = -8, then first odd integer = 2x + 1
= 2 x (-8) + 1
= -16 + 1
= -15
(ii) If x = 6, then first odd integer = 2x + 1
= 2 x 6 + 1 = 13
and second integer = 13 + 2 = 15
∴ Required integers are -15, -13, or 13, 15.
APPEARS IN
RELATED QUESTIONS
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
If the equation x2 + 4x + k = 0 has real and distinct roots, then
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve equation using factorisation method:
x2 – 10x – 24 = 0
Find three successive even natural numbers, the sum of whose squares is 308.
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
