Question

Find the values of a and b if root7-1/root7+1 - root7+1/root7-1=a +broot7

Answer 1

(√7-1/√7+1)-(√7+1/√7-1)=a+b√7
or, {(√7-1)(√7-1)-(√7+1)(√7+1)}/{(√7+1)(√7-1)}=a+b√7
or, {(√7-1)²-(√7+1)²}/{(√7)²-(1)²}=a+b√7
or, (7-2√7+1-7-2√7-1)/(7-1)=a+b√7
or, (-4√7)/6=a+b√7
or, -2√7/3=a+b√7
or, 0+(-2/3)√7=a+b√7
Equating both sides,
a=0, b=-2/3

Answer 2

Answer:

(√7-1/√7+1)-(√7+1/√7-1)=a+b√7

or, {(√7-1)(√7-1)-(√7+1)(√7+1)}/{(√7+1)(√7-1)}=a+b√7

or, {(√7-1)²-(√7+1)²}/{(√7)²-(1)²}=a+b√7

or, (7-2√7+1-7-2√7-1)/(7-1)=a+b√7

or, (-4√7)/6=a+b√7

or, -2√7/3=a+b√7

or, 0+(-2/3)√7=a+b√7

Equating both sides,

a=0, b=-2/3

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