Question

p=3+2√2 হলে দেখাও যে p√p+(1÷p√p)=10√2

Answer 1

Given :

p = 3 + 2√2

To show :

( p√p) - (1/p√p) = 10√2 .

Solution :

p = 3 + 2√2

=> p = [ 2 + 1 + 2√2]

=> p = [ {√2}² + {1}² + 2{√2}{1} ]

=> p = [ √2 + 1]²

=> √p = √[ √2 + 1]²

=> √p = | √2 + 1 |

Let us now find the value of p√p.

p√p :

=> ( 3 + 2√2 )( 1 + √2 )

=> 3 + 3√2 + 2√2 + 4

=> 7 + 5√2

Let us now find the value of 1/p√p.

1/p√p is simply the conjugate of p√p

Here, the signs are only reversed .

So , 1/p√p becomes -

=> 7 - 5√2

Required value :

( 7 + 5√2 ) - ( 7 - 5√2 )

=> 7 + 5√2 - 7 + 5√2

=> 10√2 .

This is the answer .

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

10√2Molecular mass=2*vapour density

Molecular mass=2*vapour density =2*11.2

Molecular mass=2*vapour density =2*11.2=22.4 g

Molecular mass=2*vapour density =2*11.2=22.4 gAt NTP,

Molecular mass=2*vapour density =2*11.2=22.4 gAt NTP,volume occupied by 22.4 g of gas= 22.4 l

Molecular mass=2*vapour density =2*11.2=22.4 gAt NTP,volume occupied by 22.4 g of gas= 22.4 lvolume of 11.2g gas = 22.4/22.4*11.2

Molecular mass=2*vapour density =2*11.2=22.4 gAt NTP,volume occupied by 22.4 g of gas= 22.4 lvolume of 11.2g gas = 22.4/22.4*11.2= 11.2 l$\huge{\boxed{\bold{Answer}}}$