If 1 = a ³√4 + b ³√2 + c and a, b,

Home » Aptitude » Algebra » Question

If 1 = a ³√4 + b ³√2 + c and a, b, c are rational numbers, then a + b + c is equal to
[ ³√4 + ³√2 + 1 ]

	1	= a ³√4 + b ³√2 + c
	[ ³√4 + ³√2 + 1 ]

⇒	1	= a.2^{2 / 3} + b.2^{1 / 3} + c
	( 2^{2 / 3} + 2^{1 / 3} + 1 )

⇒	( 2^{1 / 3} - 1 )	= a.2^{2 / 3} + b.2^{1 / 3} + c
	( 2^{1 / 3} - 1 )( 2^{2 / 3} + 2^{1 / 3} + 1 )

⇒	( 2^{1 / 3} - 1 )	= a.2^{2 / 3} + b.2^{1 / 3} + c
	( 2 - 1 )

[ ∵ ( a + b )(a² + b² - ab) = a³ - b³ ]
⇒ a = 0, b = 1, c = – 1
∴ a + b + c = 0 + 1 – 1 = 0

If	1	= a ³√4 + b ³√2 + c and a, b, c are rational numbers, then a + b + c is equal to
	[ ³√4 + ³√2 + 1 ]