Advertisements
Advertisements
प्रश्न
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Advertisements
उत्तर
Let the two consecutive positive odd numbers be x and (x+2).
According to the given condition
`x^2+(x+2)^2=514`
⇒`x^2+x^2+4x+4=514`
⇒`2x^2+4x-510=0`
⇒`x^2+2x-255=0`
⇒`x^2+17x-15x-255=0`
⇒`x(x+17)-15(x+17)=0`
⇒`(x+17)(x-15)=0`
⇒`x+17=0` or `x-15=0`
⇒`x=-17 or x-15`
∴`x=15` (x is a positive odd number)
When `x=15`
`x+2=15+2=17`
Hence, the required positive integers are 15 and 17.
APPEARS IN
संबंधित प्रश्न
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x
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
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Find the two consecutive natural numbers whose product is 20.
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
`x^2+8x-2=0`
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:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
Find the values of p for which the quadratic equation
Solve the following equation:
(2x+3) (3x-7) = 0
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
Solve the following equation: `1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.
The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
