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ICSE Class 10 Answered

b is the main proportion between a and b prove a2-b2+C2/a-2-b-2+c-2=b4
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Asked by kalayani822 | 09 Oct, 2023, 08:25: AM
answered-by-expert Expert Answer
Since, b is the mean proportional between a and b, we have
a/b = b/c = k
a = bk, b = ck
i.e. a = ck2, b = ck
fraction numerator straight a squared minus straight b squared plus straight c squared over denominator straight a to the power of negative 2 end exponent minus straight b to the power of negative 2 end exponent plus straight c to the power of negative 2 end exponent end fraction equals fraction numerator straight c squared straight k to the power of 4 minus straight c squared straight k squared plus straight c squared over denominator begin display style fraction numerator 1 over denominator straight c squared straight k to the power of 4 end fraction end style minus begin display style fraction numerator 1 over denominator straight c squared straight k squared end fraction end style plus begin display style 1 over straight c squared end style end fraction equals fraction numerator straight c squared open parentheses straight k to the power of 4 minus straight k squared plus 1 close parentheses over denominator begin display style 1 over straight c squared end style open parentheses begin display style 1 over straight k to the power of 4 end style minus begin display style 1 over straight k squared end style plus 1 close parentheses end fraction equals fraction numerator straight c squared open parentheses straight k to the power of 4 minus straight k squared plus 1 close parentheses over denominator begin display style 1 over straight c squared open parentheses fraction numerator 1 minus straight k squared plus straight k to the power of 4 over denominator straight k to the power of 4 end fraction close parentheses end style end fraction equals straight c to the power of 4 straight k to the power of 4 equals straight b to the power of 4
Answered by Renu Varma | 09 Oct, 2023, 10:13: AM

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