Advertisements
Advertisements
प्रश्न
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Advertisements
उत्तर
Let the two consecutive positive even numbers be x and x 2.
According to the given condition,
`x^2+(x+2)^2=452`
⇒`x^2+x^2+4x+4=452`
⇒`2x^2+4x-448=0`
⇒`x^2+2x-224=0`
⇒`x^2+16x-14x-224=0`
⇒`x(x-16)-14(x-16)=0`
⇒`(x+16)(x-14)=0`
⇒`x+16=0 or x-14=0`
⇒`x=-16 or x=14`
∴ `x=14` (x is a positive even number)
When `x=14`
`x+2=14+2=16`
Hence, the required numbers are 14 and 16.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
The sum of a numbers and its positive square root is 6/25. Find the numbers.
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
Two numbers differ by 3 and their product is 504. Find the number
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Solve : x2 – 11x – 12 =0; when x ∈ N
Solve for x: `3x^2-2sqrt3x+2=0`
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
Solve the following equation by factorization
`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0
Solve the following equation by factorization
`sqrt(x(x - 7)) = 3sqrt(2)`
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
