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Asked by g_archanasharma | 19 Mar, 2019, 22:03: PM
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begin mathsize 12px style g subscript a open parentheses x close parentheses space equals space fraction numerator a to the power of x over denominator a to the power of x plus square root of a end fraction g subscript 5 open parentheses x close parentheses plus g subscript 5 open parentheses 1 minus x close parentheses space equals space fraction numerator 5 to the power of x over denominator 5 to the power of x plus square root of 5 end fraction plus fraction numerator 5 to the power of 1 minus x end exponent over denominator 5 to the power of 1 minus x end exponent plus square root of 5 end fraction space equals space fraction numerator 5 to the power of x open parentheses 5 to the power of 1 minus x end exponent plus square root of 5 close parentheses plus 5 to the power of 1 minus x end exponent open parentheses 5 to the power of x plus square root of 5 close parentheses over denominator open parentheses 5 to the power of x plus square root of 5 close parentheses open parentheses 5 to the power of 1 minus x end exponent plus square root of 5 close parentheses end fraction equals space fraction numerator 5 plus 5 to the power of x square root of 5 plus 5 plus 5 to the power of 1 minus x end exponent square root of 5 over denominator open parentheses 5 to the power of x plus square root of 5 close parentheses open parentheses 5 to the power of 1 minus x end exponent plus square root of 5 close parentheses end fraction equals space fraction numerator 10 plus square root of 5 open parentheses 5 to the power of x space plus space 5 to the power of 1 minus x end exponent close parentheses over denominator 5 plus 5 to the power of x square root of 5 plus 5 to the power of 1 minus x end exponent square root of 5 plus 5 end root end fraction equals fraction numerator 10 plus square root of 5 open parentheses 5 to the power of x space plus space 5 to the power of 1 minus x end exponent close parentheses over denominator 10 plus square root of 5 open parentheses 5 to the power of x space plus space 5 to the power of 1 minus x end exponent close parentheses end fraction equals 1 end style
Answered by Thiyagarajan K | 25 Mar, 2019, 16:29: PM

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