Advertisements
Advertisements
प्रश्न
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
Advertisements
उत्तर
Let the required consecutive multiplies of 7 be 7x and 7(x+1)
According to the given condition,
`(7x)^2+[7(x+1)]^2=1225`
⇒`49x^2+49(x^2+2x+1)=1225`
⇒`49x^2+49x^2+98x+49=1225`
⇒`98x^2+98x-1176=0`
⇒`x^2+x-12=0`
⇒`x^2+4x-3x-12=0`
⇒`x(x+4)-3(x+4)=0`
⇒`(x+4)(x-3)=0`
⇒`x+4=0 or x-3=0`
⇒`x=-4 or x=3`
∴x=3 (Neglecting the negative value)
When x=3,
`7x=7xx3=21`
`7(x+1)=7(3+1)=7xx4=28`
Hence, the required multiples are 21 and 28.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
6x2 + 11x + 3 = 0
Divide 29 into two parts so that the sum of the squares of the parts is 425.
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
The sum of two natural number is 28 and their product is 192. Find the numbers.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
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 equation by factorisation.
2y2 + 27y + 13 = 0
Solve the following quadratic equations by factorization:
\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]
Solve the following quadratic equations by factorization: \[\frac{2}{x + 1} + \frac{3}{2(x - 2)} = \frac{23}{5x}; x \neq 0, - 1, 2\]
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following equation: 4x2 - 13x - 12 = 0
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
