Advertisements
Advertisements
Question
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
Advertisements
Solution
Let the two numbers be x and x - 4
Given that the difference of two numbers is 4.
By the given hypothesis, we have
`1/(x-4)-1/x=4/21`
`rArr(x-x+4)/(x(x-4))=4/21`
⇒ 84 = 4x(x – 4)
⇒ ๐ฅ2 - 4๐ฅ - 21 = 0
⇒ ๐ฅ2 - 7๐ฅ + 3๐ฅ - 21 = 0
⇒ ๐ฅ(๐ฅ - 7) + 3(๐ฅ - 7) = 0
⇒ (๐ฅ - 7)(๐ฅ + 3) = 0
⇒ ๐ฅ = 7 ๐๐ ๐ฅ = -3 and
If x = -3, x – 4 = -3 - 4 = -7
Hence, required numbers are 3, 7 and -3, -7
APPEARS IN
RELATED QUESTIONS
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=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 the following quadratic equations by factorization:
`(x + 3)^2 – 4(x + 3) – 5 = 0 `
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
If `sqrt (2/3)` is a solution of equation 3x2 + mx + 2 = 0, find the value of m.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
