Advertisements
Advertisements
Question
The product of two successive integral multiples of 5 is 300. Determine the multiples.
Solution
Given that the product of two successive integral multiples of 5 is 300.
Let the integers be 5x, and 5(x + 1)
Then, by the integers be 5x and 5(x + 1)
Then, by the hypothesis, we have
5x ∙ 5(x + 1) = 300
⇒ 25x (x + 1) = 300
⇒ 𝑥2 + 𝑥 = 12
⇒ 𝑥2 + 𝑥 - 12 = 0
⇒ 𝑥2 + 4𝑥 - 3𝑥 - 12 = 0
⇒ x(x + 4) -3(x + 4) = 0
⇒ (x + 4) (x – 3) = 0
⇒ x = -4 or x = 3
If x = -4, 5x = -20, 5(x + 1) = -15
x = 3, 5x = 15, 5(x + 1) = 20
∴ The two successive integral multiples are 15, 20 or -15, -20.
APPEARS IN
RELATED QUESTIONS
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Determine whether the values given against the quadratic equation are the roots of the equation.
2m2 – 5m = 0, m = 2, `5/2`
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
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.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
