The square-root of 90 + 72√2 is of the form + √2, where a and b are positive integers. The value of a+b
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Given : Square root of 90 + 72√2 is of the form a+ b√2
a and b are positive integers
To Find : Value of a and b
Solution:
Square root of 90 + 72√2 is of the form a+ b√2
Squaring both sides
=> 90 + 72√2 = a² + 2b + 2ab√2
a² + 2b = 90
2ab√2 = 72√2 => ab = 36
a² + 2b = 90
=> a < 10
ab = 36
a can be 1 , 2 , 3 , 4 , 6 , 9
None of value satisfy
Hence no possible solution for a and b being integers
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