Advertisements
Advertisements
प्रश्न
Find two consecutive natural numbers whose squares have the sum 221.
Advertisements
उत्तर
Let the number be x, x + 1
Then x2 + ( x + 1)2 = 221
⇒ x2 + x2 + 1 + 2x - 221 = 0
⇒ 2x2 + 2x - 220 = 0
⇒ x2 + x - 110 = 0
⇒ x2 + 11x - 10x - 110 = 0
⇒ x(x + 11) - 10(x + 11) = 0
⇒ (x = 11) (x - 10) = 0
⇒ x = -11 or x = 10
But x = -11 is rejected ...[∵ It cannot been as its is a natural number]
∴ x = 10
Hence, required numbers are 10, 10 + 1.
i.e., 10 and 11.
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`x^2-(sqrt2+1)x+sqrt2=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:
`100/x-100/(x+5)=1`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
If p and q are the roots of the equation x2 – px + q = 0, then ______.
Solve the following equation: (x-8)(x+6) = 0
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
