Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the smaller numbers be x
Then according to question,
The larger number be = 2x - 5, then
(2x - 5)2 - x2 = 88
4x2 - 20x + 25 - x2 - 88 = 0
3x2 - 20x - 63 = 0
3x2 - 27x + 7x - 63 = 0
3x(x - 9) + 7(x - 9) = 0
(x - 9)(3x + 7) = 0
x - 9 = 0
x = 9
Or
3x + 7 = 0
3x = -7
x = -7/3
Since, x being a positive integer so, x cannot be negative,
Therefore,
When x = 9 then larger number be
2x - 5 = 2(9) - 5 = 18 - 5 = 13
Thus, two consecutive number be either 9, 13.
RELATED QUESTIONS
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
The sum of two natural numbers is 20 while their difference is 4. Find the numbers.
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.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
The sum of the square of 2 consecutive odd positive integers is 290.Find them.
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
Solve equation using factorisation method:
`x = (3x + 1)/(4x)`
Find two consecutive positive even integers whose squares have the sum 340.
Solve the equation 3x² – x – 7 = 0 and give your answer correct to two decimal places.
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
If the product of two consecutive even integers is 224, find the integers.
Find two consecutive odd integers such that the sum of their squares is 394.
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
