Advertisements
Advertisements
Question
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
Solution
Let the numbers be x, x + 1 and x + 2 according to the given hypothesis.
๐ฅ2 + (๐ฅ + 1)2 + (๐ฅ + 2)2 = 149
⇒ ๐ฅ2 + ๐ฅ2 + 1 + 2๐ฅ + ๐ฅ2 + 4 + 4๐ฅ = 149
⇒ 3๐ฅ2 + 6๐ฅ + 5 - 149 = 0
⇒ 3๐ฅ2 + ๐ฅ - 144 = 0
⇒ ๐ฅ2 + 2๐ฅ - 48 = 0
⇒ ๐ฅ(๐ฅ + 8) - 6(๐ฅ + 8) = 0
⇒ (๐ฅ + 8)(๐ฅ - 6) = 0
⇒ x = -8 or x = 6
Considering the positive value of x
๐ฅ = 6, ๐ฅ + 1 = 7 ๐๐๐ ๐ฅ + 2 = 8
∴ The three consecutive numbers are 6, 7, 8.
APPEARS IN
RELATED QUESTIONS
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
The sum of a numbers and its positive square root is 6/25. Find the numbers.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
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 one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
