Advertisements
Advertisements
प्रश्न
Find three consecutive odd integers, the sum of whose squares is 83.
Advertisements
उत्तर
Let the three numbers be x, x + 2, x + 4
According to statements,
(x)2 + (x + 2)2 + (x + 4)2 = 83
⇒ x2 + x2 + 4x + 4 + x2 + 8x + 16 = 83
⇒ 3x2 + 12x + 20 = 83
⇒ 3x2 + 12x + 20 - 83 = 0
⇒ 3x2 + 12x - 63 = 0
⇒ x2 + 4x - 21 = 0
⇒ x2 + 7x - 3x - 21 = 0
⇒ x(x + 7) -3(x + 7) = 0
⇒ (x - 3)(x + 7) = 0
Either x - 3 = 0,
then x = 3
or
x + 7 = 0,
then x = -7
∴ Number will be 3, 3 + 2, 3 + 4 = 3, 5, 7
or
Numbers will be -7, -7 + 2, -7 + 4 = -7, -5. -3.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
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.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
The sum of natural number and its reciprocal is `65/8` Find the number
If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children.
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
