Question

IF A=3+2 ROOT 2 THEN FIND A^3+1/A^3

Answer 1

Answer:

198

Step-by-step explanation:

⇒ a = 3 + 2√2

⇒ 1/a = 1/( 3 + 2√2 )

 

    Multiply as well as divide( RHS ) by 3 - 2√2;

⇒ 1/a = (3-2√2)/(3+2√2)(3-2√2)

⇒ 1/a = (3-2√2)/[ (3)^2-(2√2)^2]

⇒ 1/a = (3-2√2)/(9-8)

⇒ 1/a = ( 3 - 2√2 ) / 1

⇒ 1/a = 3 - 2√2

     We know, a^3 + b^3 = ( a + b )^3 - 3ab( a + b )

Here,

⇒ a^3 + 1 /a^3

⇒ (a + 1/a)^3 - 3(a*1/a)(a+1/a)

⇒ (3+2√2+3-2√2)^3 - 3(1)(3+2√2+3-2√2)

⇒ (6)^3 - 3(1)(6)

⇒ 216 - 18

⇒ 198

Answer 2

A= 3+2.

so,

(3+2)^3+1/(3+2)^3

(3+2)^4/(5)^3

5^4/5^3

625/125

5.

Answer = 5.

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