Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the larger number = x
then smaller number = y
Now according to the condition,
x2 - y2 = 45 ....(i)
and y2 = 4x ....(ii)
Substituting the value of y2 from (ii) in (i)
x2 - 4x = 45
⇒ x2 - 4x - 45 = 0
⇒ x2 - 9x + 5x - 45 = 0
⇒ x(x - 9) + 5(x - 9) = 0
⇒ (x - 9)(x + 5) = 0
Either x - 9 = 0,
then x = 9
or x + 5 = 0,
then x = -5
(i) When x = 9, the larger number = 9
and smaller number
y = `sqrt(4x)`
= `sqrt(4 xx 9)`
= `sqrt(36)`
∴ y = 6
(ii) When x = -5, then larger number = -5
y = `sqrt(4x)`
= `sqrt(4 xx 5)`
= `sqrt(-20)`
which is not possible.
Hence numbers are 6, 9.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
`x^2-6x+3=0`
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
Solve the following equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
There are three consecutive positive integers such that the sum of the square of the first and the product of other two is 154. What are the integers?
