Two numbers A and b are in the ratio 2 is to 3 the difference between the square of a and b is 45 find a b
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The required numbers are 9 and 6.
Given:
Two numbers a and b are in the ratio 2: 3
The difference between the squares of a and b is 45
To find:
Find a and b
Solution:
Given that a and b are in the ratio 2: 3
Let the numbers be 2x and 3x
[ Since a and b are in 2: 3 ratio ]
=> a = 2x and b = 3x
Given that difference between squares of a and b is 45
=> (3x)² - (2x)² = 45
=> 9x² - 4x² = 45
=> 5x² = 45
=> x² = 45/5
=> x² = 9
=> x² = 3² [ ∵ 9 = 3² ]
The value of x = 3
The number, a = 2x = 2(3) = 6
The number, b = 3x = 3(3) = 9
Therefore,
The required numbers are 9 and 6.
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