Advertisements
Advertisements
प्रश्न
Find two consecutive odd integers such that the sum of their squares is 394.
Advertisements
उत्तर
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
संबंधित प्रश्न
Two numbers differ by 3 and their product is 504. Find the number
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]
If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
