If a=1/7+4root3 b=1/7-4root3 find the value of( a )square +(b) square
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a=1/(7+4√3)
a=1/(7+4√3)×(7-4√3)/(7-4√3)
a=(7-4√3)/(7+4√3)(7-4√3)
a=(7-4√3)/(49-48)
a=7-4√3................................................1
and,
b=1/(7-4√3)
b=1/(7-4√3)×(7+4√3)/(7+4√3)
b=(7+4√3)/(7-4√3)(7+4√3)
b=(7+4√3)/(49-48)
b=7+4√3..............................................2
Now,
=a²+b²
=(7-4√3)²+(7+4√3)² (by eq1 and eq2)
=49+48-56√3+49+48+56√3
=98+96
=194
Hence , a²+b²=194
a=1/(7+4√3)×(7-4√3)/(7-4√3)
a=(7-4√3)/(7+4√3)(7-4√3)
a=(7-4√3)/(49-48)
a=7-4√3................................................1
and,
b=1/(7-4√3)
b=1/(7-4√3)×(7+4√3)/(7+4√3)
b=(7+4√3)/(7-4√3)(7+4√3)
b=(7+4√3)/(49-48)
b=7+4√3..............................................2
Now,
=a²+b²
=(7-4√3)²+(7+4√3)² (by eq1 and eq2)
=49+48-56√3+49+48+56√3
=98+96
=194
Hence , a²+b²=194
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