Advertisements
Advertisements
प्रश्न
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
Advertisements
उत्तर
Let the two digits be:
Tens digits be x and units = 16/x
Number `=10x+16/x`
Number obtained by interchanging `=10xx16/x+x`
`rArr(10x+16/x)-(10xx16/x+x)=54`
`rArr10x+16/7-160/x+x=54`
⇒ 10x2 + 16 - 160 - x2 = 54x
⇒ 9x2 - 54x - 144 = 0
⇒ x2 - 6x - 16 = 0
⇒ x2 - 8x + 2x - 16 = 0
⇒ x(x - 8) + 2(x - 8) = 0
⇒ (x - 8)(x + 2) = 0
⇒ x - 8 = 0
⇒ x = 8
Or
⇒ x + 2 = 0
⇒ x = -2
But, a digit can never be negative, hence x = 8
Hence the required number `=10x+16/x=10(8)+16/8=80+2=82`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve the following quadratic equations by factorization:
`x^2 – (a + b) x + ab = 0`
Solve the following quadratic equations by factorization:
`(x-3)/(x+3 )+(x+3)/(x-3)=2 1/2`
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
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 the equation x2 − bx + 1 = 0 does not possess real roots, then
If one of the equation x2 + ax + 3 = 0 is 1, then its other root is
Solve equation using factorisation method:
x(x – 5) = 24
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the following equation by factorization
x2 – 3x – 10 = 0
Solve the following equation by factorization
x(2x + 5) = 3
In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
Find the roots of the following quadratic equation by the factorisation method:
`3sqrt(2)x^2 - 5x - sqrt(2) = 0`
