QUADRATIC �EQUATIONS
or x – 6 = 0
or x = 6
x = – 8
∴
Q The sum of the squares of two consecutive even natural numbers is 100. Find the numbers.
Sol.
As per the given condition,
+
( )2
=
100
x2 +
2x2
2x2
x2
x2
∴
∴
∴
∴
∴
(Dividing throughout by 2)
x2 + 4x + 4
x
(x + 8)
x + 8 = 0
∴
∴
∴
Let the two consecutive even natural numbers be x and x+2.
( )2
x
x+2
(a+b)2 = a2 + 2ab + b2
The required numbers are natural numbers
x ≠ -8
Hence, x = 6
∴
∴
and x + 2
The two required consecutive even natural numbers are 6 and 8.
∴
How to assume two consecutive even natural numbers ?
x and x + 2
Means +
Means (something)2
Square of what ?
How many numbers?
1
Find two factors of 48 in such a way that by subtracting factors we get middle number 2
8
6
48
+
–
6
–
= 2
8
+ 8x
– 6x
– 48
= 0
(x + 8)
– 6
(x + 8)
= 0
(x – 6)
= 0
= 6 + 2
= 8
= 100
+ 4x
+ 4
– 100
= 0
What we need to find ?
Since we are subtracting the factors give middle term sign to the bigger factor and the opposite sign to the smaller factor
+ 4x
– 96
= 0
+ 2x
– 48
= 0
homework