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Express-15-35-21-5-3-2-5-7-in-the-form-a-3-b-7-

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Question Number 148525 by nadovic last updated on 28/Jul/21
Express (((√(15))+(√(35))+(√(21))+5)/( (√3)+2(√5)+(√7))) in the form a(√(3 ))+ b(√7).
Express15+35+21+53+25+7intheforma3+b7.
Answered by Ar Brandon last updated on 28/Jul/21
(((√(15))+(√(35))+(√(21))+5)/( (√3)+2(√5)+(√7))) =(((√3)∙(√5)+(√7)∙(√5)+(√3)∙(√7)+(√5) ^2 )/( (√3)+2(√5)+(√7))) =(((√5) ^2 +((√3)+(√7))(√5)+(√7)∙(√5))/( (√3)+2(√5)+(√7))) =((((√5)+(√3))((√5)+(√7)))/(((√5)+(√3))+((√5)+(√7))))×((((√5)+(√3))−((√5)+(√7)))/(((√5)+(√3))−((√5)+(√7))))
15+35+21+53+25+7=3⋅5+7⋅5+3⋅7+523+25+7=52+(3+7)5+7⋅53+25+7=(5+3)(5+7)(5+3)+(5+7)×(5+3)−(5+7)(5+3)−(5+7)
Answered by MJS_new last updated on 29/Jul/21
((5+(√7)(√5)+(√7)(√3)+(√5)(√3))/( (√7)+2(√5)+(√3)))= =(((5+(√7)(√5)+(√7)(√3)+(√5)(√3))(−(√7)+2(√5)+(√3)))/(((√7)+2(√5)+(√3))(−(√7)+2(√5)+(√3))))= =((2(√7)(√5)(√3)+8(√7)+6(√5)+8(√3))/(16+4(√5)(√3)))= =(((√7)(√5)(√3)+4(√7)+3(√5)+4(√3))/(2(4+(√5)(√3))))= =((((√7)(√5)(√3)+4(√7)+3(√5)+4(√3))(4−(√5)(√3)))/(2(4+(√5)(√3))(4−(√5)(√3))))= =(((√7)+(√3))/2) ⇒ a=b=(1/2)
5+75+73+537+25+3==(5+75+73+53)(−7+25+3)(7+25+3)(−7+25+3)==2753+87+65+8316+453==753+47+35+432(4+53)==(753+47+35+43)(4−53)2(4+53)(4−53)==7+32⇒a=b=12
Commented by nadovic last updated on 30/Jul/21
Thank you Sir
ThankyouSir

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