Advertisements
Advertisements
प्रश्न
Find the two consecutive positive even integers whose product is 288.
Advertisements
उत्तर
Let the two consecutive positive even integers be x and(x+2)
According to the given condition,
`x(x+2)=288`
⇒`x^2+2x-288=0`
⇒`x^2+18x-16x-288=0`
⇒`x(x+18)-16(x+18)=0`
⇒`(x+18)(x-16)=0`
⇒`x+18=0 or x-16=0`
⇒`x=-18 or x=16`
`∴x=16 ` (x is a positive even integer)
When` x=16 `
`x+2=16+2=18`
Hence, the required integers are 16 and 18.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
Find the two consecutive natural numbers whose product is 20.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve the following quadratic equations by factorization:
`4/(x+2)-1/(x+3)=4/(2x+1)`
The sum of the squares of two consecutive positive integers is 365. Find the integers.
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
Solve the following equation: `("x" + 3)/("x" - 2) - (1 - "x")/"x" = 17/4`
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
The sum of the numerator and denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by `(4)/(35)`. Find the fraction.
If the sum of two smaller sides of a right – angled triangle is 17cm and the perimeter is 30cm, then find the area of the triangle.
The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
