Advertisements
Advertisements
प्रश्न
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Advertisements
उत्तर
Let the tens digit be x
Then, the units digit = 12/x
`therefore " Number" =10x+12/x`
And, number obtained by interchanging the Digits `= 10xx12/x+x=120/x+x`
`rArr10x+12/x+36=120/x+x`
`rArr9x+(12-120)/x+36=0`
⇒ 9x2 - 108 + 36x = 0
⇒ 9(x2 + 4x - 12) = 0
⇒ x2 + 6x - 2x - 12 = 0
⇒ x(x + 6) - 2(x + 6) = 0
⇒ (x - 2)(x + 6) = 0
∴ x = 2 or x = -6
But, a digit can never be negative, x = 2
Hence, the digit `=10x+12/x=10(2)+12/2=20+6=26`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
Solve the following quadratic equations by factorization:
`(x + 3)^2 – 4(x + 3) – 5 = 0 `
`8x^2-14x-15=0`
Solve the following quadratic equation by
factorisation.
5m2 = 22m + 15
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
Solve the following equation: abx2 +(b2-ac) x - bc = 0
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
A two digit number is such that the product of its digit is 14. When 45 is added to the number, then the digit interchange their places. Find the number.
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
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.
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.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
