CBSE Class 9 Answered

(2-√3)-³ + (2+√3)-³

Asked by kumarik23731 | 22 Nov, 2023, 10:50: PM

Expert Answer

Let us use the following formulae

begin mathsize 14px style open parentheses a plus b close parentheses cubed space equals space a cubed plus 3 a b left parenthesis a plus b right parenthesis plus b cubed end style

begin mathsize 14px style open parentheses a minus b close parentheses cubed space equals space a cubed minus 3 a b left parenthesis a minus b right parenthesis minus b cubed end style

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begin mathsize 14px style open parentheses 2 minus square root of 3 close parentheses cubed space equals space 2 cubed space minus space 3 space cross times space 2 space cross times square root of 3 space left parenthesis space 2 space minus space square root of 3 space right parenthesis space minus space left parenthesis space square root of 3 space right parenthesis cubed space equals space 26 space minus 15 square root of 3 end style

begin mathsize 14px style 1 over open parentheses 2 minus square root of 3 close parentheses cubed space equals space fraction numerator 1 over denominator left parenthesis space 26 minus 15 square root of 3 space right parenthesis end fraction space equals space fraction numerator 1 over denominator left parenthesis space 26 minus 15 square root of 3 space right parenthesis end fraction cross times fraction numerator left parenthesis space 26 plus 15 square root of 3 space right parenthesis over denominator left parenthesis space 26 plus 15 square root of 3 space right parenthesis end fraction space equals space fraction numerator left parenthesis space 26 plus 15 square root of 3 space right parenthesis over denominator 1 end fraction end style

begin mathsize 14px style open parentheses 2 plus square root of 3 close parentheses cubed space equals space 2 cubed space plus space 3 space cross times space 2 space cross times square root of 3 space left parenthesis space 2 space plus space square root of 3 space right parenthesis space plus space left parenthesis space square root of 3 space right parenthesis cubed space equals space 26 space plus 15 square root of 3 end style

begin mathsize 14px style 1 over open parentheses 2 plus square root of 3 close parentheses cubed space equals space fraction numerator 1 over denominator left parenthesis space 26 plus 15 square root of 3 space right parenthesis end fraction space equals space fraction numerator 1 over denominator left parenthesis space 26 plus 15 square root of 3 space right parenthesis end fraction cross times fraction numerator left parenthesis space 26 minus 15 square root of 3 space right parenthesis over denominator left parenthesis space 26 minus 15 square root of 3 space right parenthesis end fraction space equals space fraction numerator left parenthesis space 26 minus 15 square root of 3 space right parenthesis over denominator 1 end fraction end style

begin mathsize 14px style 1 over open parentheses 2 minus square root of 3 close parentheses cubed space plus space 1 over open parentheses 2 plus square root of 3 close parentheses cubed space equals space 26 space plus space 15 square root of 3 space plus 26 space minus space 15 square root of 3 space equals space 52 end style

Answered by Thiyagarajan K | 23 Nov, 2023, 10:55: AM

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