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:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Find the consecutive numbers whose squares have the sum 85.
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
`x^2-6x+3=0`
Solve the following quadratic equation by
factorisation.
5m2 = 22m + 15
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Solve the following equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
Find the values of x if p + 1 =0 and x2 + px – 6 = 0
Find two consecutive natural numbers such that the sum of their squares is 61.
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
