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 for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
Solve the following quadratic equations by factorization:
48x2 − 13x − 1 = 0
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Solve each of the following equations by factorization:
`x+1/x=2.5`
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
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: 4x2 + 16x = 0
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
A wire ; 112 cm long is bent to form a right angled triangle. If the hypotenuse is 50 cm long, find the area of the triangle.
