Algebra Easy Questions and Answers

Using Rule 9,
Expression = ³√p( p² - 3p + 3 ) - 1
Expression = ³√( p³ - 3p² + 3p - 1
Expression = ³√(p - 1)³ = p - 1
Expression = 101 – 1 = 100

Correct Option: A

Using Rule 9,
Expression = ³√p( p² - 3p + 3 ) - 1
Expression = ³√( p³ - 3p² + 3p - 1
Expression = ³√(p - 1)³ = p - 1
Expression = 101 – 1 = 100

Using Rule 8,
Expression = ³√p( p² + 3p + 3 ) + 1
Expression = ³√( p³ + 3p² + 3p + 1
Expression = ³√(p + 1)³ = [ ( p + 1 )³ ]^{1 / 3} = ( p + 1 )
When p = 124,
Expression = p + 1 = 124 + 1 = 125

Correct Option: D

Using Rule 9,
p – 2q = 4
On cubing both sides,
(p – 2q)³ = 64
⇒ p³ - 8q³ + 3p.4q² - 3p².2q = 64
⇒ p³ - 8q³ + 12pq² - 6p²q = 64
⇒ p³ - 8q³ + 6pq(p – 2q) = 64
⇒ p³ - 8q³ + 6pq × 4 = 64
⇒ p³ - 8q³ – 24pq – 64 = 0

Correct Option: B

Expression =			x² + y² + xy
			x³ - y³

Expression =	x² + y² + xy	=	1
	(x - y)(x² + y² + xy)		(x - y)

Expression =	1	= 1
	19 - 18

Correct Option: A

Expression =			x² + y² + xy
			x³ - y³

Expression =	x² + y² + xy	=	1
	(x - y)(x² + y² + xy)		(x - y)

Expression =	1	= 1
	19 - 18

x +	1	= 2
	x

⇒ x² - 2x + 1 = 0
⇒ ( x - 1 )² = 0 ⇒ x = 1

∴ x¹⁷ +	1	= 1 + 1 = 2
	x¹⁹

Second Method :-

Here, x +	1	= 2
	x

By Hit and trial method , putting x = 1

∴ x¹⁷ +	1	= 2
	x¹⁹

Correct Option: C

x +	1	= 2
	x

⇒ x² - 2x + 1 = 0
⇒ ( x - 1 )² = 0 ⇒ x = 1

∴ x¹⁷ +	1	= 1 + 1 = 2
	x¹⁹

Second Method :-

Here, x +	1	= 2
	x

By Hit and trial method , putting x = 1

∴ x¹⁷ +	1	= 2
	x¹⁹

If x +	1	= 2 and x is real, then the value of x¹⁷ +		1	is
	x			x¹⁹

If x = 19 and y = 18, then the value of			x² + y² + xy			is :
			x³ - y³

Algebra

Algebra

Aptitude

Correct Option: A

Correct Option: D

Correct Option: B

Correct Option: A

Correct Option: C