Advertisements
Advertisements
Question
The product of two successive integral multiples of 5 is 300. Determine the multiples.
Advertisements
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
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Solve the following quadratic equations by factorization:
6x2 + 11x + 3 = 0
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
Find the consecutive even integers whose squares have the sum 340.
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
The sum of two natural number is 28 and their product is 192. Find the numbers.
Solve the following quadratic equation by factorisation.
3x2 - 2√6x + 2 = 0
Find the value of p for which the quadratic equation
\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.
Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
Solve the following equation: 3x2 + 25 x + 42 = 0
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
Solve equation using factorisation method:
`x + 1/x = 2.5`
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
Solve the following equation by factorization
x2– 4x – 12 = 0,when x∈N
Solve the following equation by factorization
`x + (1)/x = 2(1)/(20)`
If the product of two positive consecutive even integers is 288, find the integers.
The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
