CBSE Class 9 Answered

If a + b x √3 equals to 2 into root 3 minus 2 upon 2 root 3 + 2 find values of a and b

Asked by singha83147 | 04 Oct, 2023, 21:28: PM

Expert Answer

begin mathsize 14px style a space plus space b square root of 3 space equals space 2 square root of 3 space minus space fraction numerator 2 over denominator 2 square root of 3 space plus space 2 end fraction end style

begin mathsize 14px style a space plus space b square root of 3 space equals space 2 square root of 3 space minus space fraction numerator 1 over denominator square root of 3 space plus space 1 end fraction end style

begin mathsize 14px style a space plus space b square root of 3 space equals space space fraction numerator 2 square root of 3 space left parenthesis space square root of 3 space plus 1 space right parenthesis space minus space 1 over denominator square root of 3 space plus space 1 end fraction end style

begin mathsize 14px style a space plus space b square root of 3 space equals space space fraction numerator 6 plus 2 square root of 3 space minus 1 space over denominator square root of 3 space plus space 1 end fraction space equals space fraction numerator 5 plus 2 square root of 3 over denominator square root of 3 plus 1 end fraction end style

begin mathsize 14px style a space plus space b square root of 3 space equals space fraction numerator 5 plus 2 square root of 3 over denominator square root of 3 plus 1 end fraction space cross times fraction numerator square root of 3 space minus 1 over denominator square root of 3 space minus 1 end fraction space equals space fraction numerator open parentheses 5 plus 2 square root of 3 close parentheses cross times open parentheses square root of 3 space minus 1 close parentheses over denominator 2 end fraction space equals space fraction numerator 3 square root of 3 plus 1 over denominator 2 end fraction end style

begin mathsize 14px style a space plus space b square root of 3 space equals 1 half space plus 3 over 2 square root of 3 end style

By comparing LHS and RHS , we get a = 1/2 and b = 3/2

Answered by Thiyagarajan K | 05 Oct, 2023, 07:38: AM

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