The sum of two numbers is 90, and their product is 1800. What are the numbers?
Explain with process;
Aaryadeep:
you need to give a hint or value of one number
The hint is not required. Its basic algebra.
use the expreseeion ax^2+bx+c=0
Answers
Answered by
0
let first no.=x
second no.=y
ATQ x+y=90
x=90-y
xy=1800
put x=90-y in xy=1800
second no.=y
ATQ x+y=90
x=90-y
xy=1800
put x=90-y in xy=1800
Answered by
1
Hi there!
There are different methods to solve this. I'll show you one way. You'll understand it if you've studied algebraic identities. (Just comment down below if you haven't and I'll explain.)
Let the numbers be a and b.
So we've a+b = 90
and ab= 1800
(a+b)^2 = (90)^2
=> a^2 + b^2 + 2ab = 8100
(Subtracting 4ab from both sides to obtain an equation a-b)
=> a^2+b^2+2ab-4ab = 8100 - 4 × 1800 (ab = 1800)
=> a^2+b^2 - 2ab = 900
=> (a-b)^2 = 900
=> a-b = 30
We know, a+b = 90...(1)
a-b = 30...(2)
Combining equations (1) and (2)
=> a+b+a-b = 90+30
=> 2a = 120 => a = 60
Finding b, a - b = 30 => 60-b= 30 => b = 30
So the numbers are 60 and 30.
There are different methods to solve this. I'll show you one way. You'll understand it if you've studied algebraic identities. (Just comment down below if you haven't and I'll explain.)
Let the numbers be a and b.
So we've a+b = 90
and ab= 1800
(a+b)^2 = (90)^2
=> a^2 + b^2 + 2ab = 8100
(Subtracting 4ab from both sides to obtain an equation a-b)
=> a^2+b^2+2ab-4ab = 8100 - 4 × 1800 (ab = 1800)
=> a^2+b^2 - 2ab = 900
=> (a-b)^2 = 900
=> a-b = 30
We know, a+b = 90...(1)
a-b = 30...(2)
Combining equations (1) and (2)
=> a+b+a-b = 90+30
=> 2a = 120 => a = 60
Finding b, a - b = 30 => 60-b= 30 => b = 30
So the numbers are 60 and 30.
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