Advertisements
Advertisements
Question
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Advertisements
Solution
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
RELATED QUESTIONS
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Find the roots of the following quadratic equation by factorisation:
`2x^2 – x + 1/8 = 0`
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
3x2 − 14x − 5 = 0
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
