Advertisements
Advertisements
Question
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Solution
Let these two numbers be X and Y, Y being the bigger number. Then as per the question,
X2+Y2= 208 ..... (i)
Y2 = 18X ..... (ii)
From (i), we get Y2= 208 - X2. Putting this in (ii), we get
208 - X2 = 18X
⇒ x2 + 18X - 208 = 0
⇒ X2 + 26X - 8X - 208 = 0
⇒ X(X + 26) - 8(X + 26) = 0
⇒ (X-8) (X+ 26) = 0
⇒ X can't be a negative number , hence X=8
⇒ Putting X=8 in (ii), we get Y2 = 18 x 8=144
⇒ Y= l 2
⇒ X=8 and Y = 12.
APPEARS IN
RELATED QUESTIONS
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
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 each of the following equations by factorization:
`9/2x=5+x^2`
Find two consecutive multiples of 3 whose product is 648.
Find the two consecutive positive even integers whose product is 288.
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solve the following equation : 5x2 - 11x + 2 = 0
Solve the following : `("x" - 1/2)^2 = 4`
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
