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:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
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.
Find the consecutive even integers whose squares have the sum 340.
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equations by factorization: \[2 x^2 + ax - a^2 = 0\]
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
Solve the following equation : 5x2 - 11x + 2 = 0
Solve equation using factorisation method:
(x + 1)(2x + 8) = (x + 7)(x + 3)
Solve the following equation by factorization
3(x – 2)2 = 147
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
