Advertisements
Advertisements
प्रश्न
The sum of natural number and its positive square root is 132. Find the number.
Advertisements
उत्तर
Let the required natural number be x.
According to the given condition,
`x+sqrtx=132`
Putting sqrtx=y or x=y^2, we get
`y^2+y=132`
⇒`y^2+y-132=0`
⇒`y^2+12y-11y-132=0`
⇒`y(y+12)-11(y+12)=0`
⇒`(y+12)(y-11)=0`
⇒`y+12=0 or y-11=0`
⇒`y=-12 or y=11`
∴ `y=11` ( y cannot be negative)
Now,
`sqrtx=11`
⇒` x=(11)^2=121`
Hence, the required natural number is 121.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
`2x^2+5x-3=0`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
If the equation x2 + 4x + k = 0 has real and distinct roots, then
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
If one of the equation ax2 + bx + c = 0 is three times times the other, then b2 : ac =
Solve the following equation: (x-8)(x+6) = 0
Solve the following equation: `1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Solve the following equation by factorization
x2 – 3x – 10 = 0
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
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.
Find the roots of the following quadratic equation by the factorisation method:
`2x^2 + 5/3x - 2 = 0`
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
