17th sum

Asked by lovemaan5500 | 25th Jan, 2019, 03:53: PM

Expert Answer:

begin mathsize 16px style left parenthesis straight x plus straight a right parenthesis to the power of straight n
equals straight C presuperscript straight n subscript 0 straight x to the power of straight n plus straight C presuperscript straight n subscript 1 straight x to the power of straight n minus 1 end exponent straight a plus straight C presuperscript straight n subscript 2 straight x to the power of straight n minus 2 end exponent straight a squared plus straight C presuperscript straight n subscript 3 straight x to the power of straight n minus 3 end exponent straight a cubed..... plus straight C presuperscript straight n subscript straight n straight a to the power of straight n
equals open parentheses straight C presuperscript straight n subscript 0 straight x to the power of straight n plus straight C presuperscript straight n subscript 2 straight x to the power of straight n minus 2 end exponent straight a squared plus.... close parentheses plus open parentheses straight C presuperscript straight n subscript 1 straight x to the power of straight n minus 1 end exponent plus straight C presuperscript straight n subscript 3 straight x to the power of straight n minus 3 end exponent straight a cubed plus..... close parentheses
equals space straight P space plus space straight Q space...... left parenthesis straight i right parenthesis
left parenthesis straight x minus straight a right parenthesis to the power of straight n
equals straight C presuperscript straight n subscript 0 straight x to the power of straight n minus straight C presuperscript straight n subscript 1 straight x to the power of straight n minus 1 end exponent straight a plus straight C presuperscript straight n subscript 2 straight x to the power of straight n minus 2 end exponent straight a squared minus straight C presuperscript straight n subscript 3 straight x to the power of straight n minus 3 end exponent straight a cubed..... plus straight C presuperscript straight n subscript straight n open parentheses negative 1 close parentheses to the power of straight n straight a to the power of straight n
equals open parentheses straight C presuperscript straight n subscript 0 straight x to the power of straight n plus straight C presuperscript straight n subscript 2 straight x to the power of straight n minus 2 end exponent straight a squared plus.... close parentheses minus open parentheses straight C presuperscript straight n subscript 1 straight x to the power of straight n minus 1 end exponent plus straight C presuperscript straight n subscript 3 straight x to the power of straight n minus 3 end exponent straight a cubed plus..... close parentheses space
equals straight P minus straight Q space....... left parenthesis ii right parenthesis
straight i right parenthesis
LHS space equals straight P squared minus straight Q squared
equals left parenthesis straight P plus straight Q right parenthesis left parenthesis straight P minus straight Q right parenthesis
equals left parenthesis straight x plus straight a right parenthesis to the power of straight n left parenthesis straight x minus straight a right parenthesis to the power of straight n
equals open square brackets left parenthesis straight x plus straight a right parenthesis left parenthesis straight x minus straight a right parenthesis close square brackets to the power of straight n
equals left parenthesis straight x squared minus straight a squared right parenthesis to the power of straight n
equals RHS
ii right parenthesis
4 PQ space equals space open parentheses straight P plus straight Q close parentheses squared minus space open parentheses straight P minus straight Q close parentheses squared
equals open square brackets left parenthesis straight x plus straight a right parenthesis to the power of straight n close square brackets squared minus open square brackets left parenthesis straight x minus straight a right parenthesis to the power of straight n close square brackets squared
equals left parenthesis straight x plus straight a right parenthesis to the power of 2 straight n end exponent minus left parenthesis straight x minus straight a right parenthesis to the power of 2 straight n end exponent
equals RHS
iii right parenthesis
LHS equals 2 open parentheses straight P squared plus straight Q squared close parentheses
equals space open parentheses straight P plus straight Q close parentheses squared plus space open parentheses straight P minus straight Q close parentheses squared
equals open square brackets left parenthesis straight x plus straight a right parenthesis to the power of straight n close square brackets squared plus open square brackets left parenthesis straight x minus straight a right parenthesis to the power of straight n close square brackets squared
equals left parenthesis straight x plus straight a right parenthesis to the power of 2 straight n end exponent plus left parenthesis straight x minus straight a right parenthesis to the power of 2 straight n end exponent
equals RHS



end style

Answered by Sneha shidid | 25th Jan, 2019, 05:03: PM