QUADRATIC EQUATIONS
18 - 10
=
8
Q.The difference of squares of two numbers is 180. The square of
the smaller number is 8 times the larger number. Find the two numbers.
Sol :
Let larger number be ‘x’
(Smaller no.)2
∴
Smaller no
As per the given condition
x2
= 180
∴ x2
– 18x
+ 10x
– 180
= 0
∴ x
+ 10
= 0
∴ (x – 18)
(x + 10)
= 0
∴
(x – 18)
= 0
or
(x + 10)
= 0
∴
x = 18
or
x = – 10
If larger number is 18
∴
Smaller no
If larger number is – 10
∴
Smaller no
∴
It is not acceptable
∴
The larger no is 18 and the smaller no is 12
What we need to find in this sum ?
It is given that ….
In a comparative statement whatever comes later is taken as ‘x’
=
8x
=
∴ x2
– 8x
– 180
= 0
1
Calculation
180
90
45
2
2
3
15
3
5
5
1
Find two factors of 180 in such a way that by subtracting factors we get middle no.
Let’s do prime factorization of 180
Since last sign is ‘-’ Give middle sign to the bigger factor & opposite sign to smaller factor.
18
10
180
–
+
(x – 18)
(x – 18)
18 – 10 = 8
‘-’ sign means subtracting
180 × 1 = 180
–
(Larger no.)2 – (smaller no.)2 = 180
x2
–
8x
= 180
EX 4.3 7