If (√3-√2-√1)(√3+√2+√1) = a√3 +b√2 +c√1 then find the value of (a + b + c)
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Step-by-step explanation:
Given a=
3−2
2
1
=
9−8
3+2
2
=3+2
2
[on rationalizing]
b=
3+2
2
1
=
9−8
3−2
2
=3−2
2
now a
3
+b
3
=(a+b)
3
−3ab(a+b)
=(3+2
2
+3−2
2
)
2
−3(3+2
2
)(3−2
2
)[3+2
2
+3−2
2
]
=(6)
3
−3(9−8)[6]
=216 - 18
[a
3
+b
3
=198]
Here value of [a
3
+b
3
=198]
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