If $$(a + b \sqrt{n})$$ is the positive square root of $$(29 - 12\sqrt{5})$$, where a and b are integers, and

Question

If $$(a + b \sqrt{n})$$ is the positive square root of $$(29 - 12\sqrt{5})$$, where a and b are integers, and n is a natural number, then the maximum possible value of $$(a + b + n)$$ is

Accepted Answer

18. ( a + b n ) (a + b \sqrt{n}) ( a + b n ​ ) is the positive square root of ( 29 − 12 5 ) (29 - 12\sqrt{5}) ( 29 − 12 5 ​ ) So 29 − 12 5 = ( a + b n ) 2 29-12\sqrt{5}=\left(a+b\sqrt{n}\right)^2 29 − 12 5 ​ = ( a + b n ​ ) 2 29 − 12 5 = a 2 + b 2 n + 2 a b n 29-12\sqrt{5}=a^2+b^2n+2ab\sqrt{n} 29 − 12 5

If $(a + b \sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$ , where a and b are integers, and n is a natural number, then the maximum possible value of $(a + b + n)$ is

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If (a+bn)(a + b \sqrt{n})(a+bn​) is the positive square root of (29−125)(29 - 12\sqrt{5})(29−125​), where a and b are integers, and n is a natural number, then the maximum possible value of (a+b+n)(a + b + n)(a+b+n) is

If $(a + b \sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$ , where a and b are integers, and n is a natural number, then the maximum possible value of $(a + b + n)$ is

If $(a + b \sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$ , where a and b are integers, and n is a natural number, then the maximum possible value of $(a + b + n)$ is