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Answers
Answer:
Step-by-step explanation:
25) = 54 - 27 - 33 + 6 = 60 - 60 = 0
So, 3 is the factor of p ( x ).
Now ,dividing p ( x ) by ( x - 3 ) and ( x + 2 ),we get
(2x + 1 ).
Therefore, the factors of p ( x ) are ( x - 3 ) (x + 2 ) ( 2x+ 1 ).
26) Given that,
x = ( 2 + √5 )
Squaring on both sides, we get
x² = ( 2 + √5 )²
= ( 2 )² + ( √5 )² + 2 ( 2 ) ( √5)
= 4 + 5 + 4√5
= 9 + 4√5.
1/x² = 1/ ( 9 + 4√5 )
= 1/ ( 9+ 4√5 ) × (9- 4√5) / ( 9- 4√5) (∵Rationalising ththe denominator)
= ( 9- 4√5 ) / ( 9 )² - ( 4√5)² [∵a² - b² = (a - b ) (a + b) ]
= ( 9 - 4√5) / 81 - 80 (∵ (4√5)² = (4)² × ( √5)² = 16 × 5 = 80 )
= ( 9- 4√5)/ 1
= 9- 4√5.
∴ x² + 1/x² = 9+ 4√5+ 9- 4√5
= 9 + 9
= 18 is the answer.
14) Curved surface area of a cone = πrπrl
Here, Height = h = 16 cm and radius = r = 12 cm.
Let the slant height be l.
We know that,
l² = h² + r²
= ( 16 )² + ( 12 )²
= 256 + 144
= 400
l = √400 = √(20)² = 20 cm.
∴Curved surface area of the cone
= πrl
= 3.14 × 12 × 20 cm²
= 753.6 cm².
∴Volume of a cone
= 1/3 πr²h
= 1/3 × 3.14 × 12 × 12 × 16
= 2411.52 cm³. is the answer.
