Advertisements
Advertisements
Question
Two numbers differ by 3 and their product is 504. Find the number
Solution
Let the two numbers be x and x - 3 given that x(x + 3) = 504
⇒ x2 + 3x - 504 = 0
⇒ x2 + 24x - 21x - 504 = 0
⇒ x(x + 24) - 21(x + 24) = 0
⇒ (x + 24)(x - 21) = 0
Therefore,
⇒ x + 24 = 0
⇒ x = -24
Or
⇒ x - 21 = 0
⇒ x = 21
Since, x being a number,
Therefore,
When x = -24 then
x + 3 = -24 + 3 = -21
And when x = 21 then
x + 3 = 21 + 3 = 24
Thus, two consecutive numbers be either 21, 24 or -21, -24.
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
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.
Solve 2x2 – 9x + 10 =0; when x ∈ Q
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
Solve the following equation: `10"x" - 1/"x" = 3`
There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
The hotel bill for a number of people for an overnight stay is Rs. 4800. If there were 4 more, the bill each person had to pay would have reduced by Rs. 200. Find the number of people staying overnight.
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
