Advertisements
Advertisements
рдкреНрд░рд╢реНрди
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
рдЙрддреНрддрд░
Let the numbers be x, x + 1 and x + 2 according to the given hypothesis.
ЁЭСе2 + (ЁЭСе + 1)2 + (ЁЭСе + 2)2 = 149
⇒ ЁЭСе2 + ЁЭСе2 + 1 + 2ЁЭСе + ЁЭСе2 + 4 + 4ЁЭСе = 149
⇒ 3ЁЭСе2 + 6ЁЭСе + 5 - 149 = 0
⇒ 3ЁЭСе2 + ЁЭСе - 144 = 0
⇒ ЁЭСе2 + 2ЁЭСе - 48 = 0
⇒ ЁЭСе(ЁЭСе + 8) - 6(ЁЭСе + 8) = 0
⇒ (ЁЭСе + 8)(ЁЭСе - 6) = 0
⇒ x = -8 or x = 6
Considering the positive value of x
ЁЭСе = 6, ЁЭСе + 1 = 7 ЁЭСОЁЭСЫЁЭСС ЁЭСе + 2 = 8
∴ The three consecutive numbers are 6, 7, 8.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solve for x : 12abx2 – (9a2 – 8b2 ) x – 6ab = 0
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 natural number is 28 and their product is 192. Find the numbers.
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
Solve equation using factorisation method:
2(x2 – 6) = 3(x – 4)
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
