Question

1 by a + b + x is equal to 1 by a + 1 by b + 1 by X

Answer 1

It is given that 1 / ( a + b + x ) = 1 / a + 1 / b + 1 / x

$\implies \dfrac{1}{a + b + x} = \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{x}$


Adding - 1 / x on both sides,

$\implies \dfrac{1}{a + b + x} - \dfrac{1}{x} = \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{x} - \dfrac{1}{x} \\ \\ \\ \implies\dfrac{x - (a + b + x)}{(a + b + x)x} = \dfrac{1}{a} + \dfrac{1}{b} \\ \\ \\ \implies \dfrac{x - a - b - x}{(a + b + x)x} = \dfrac{a + b}{ab} \\ \\ \\ \implies \dfrac{x - a - b - x}{(a + b + x)x} = \dfrac{a + b}{ab} \\ \\ \\ \implies\dfrac{ - a - b }{(a + b + x)x} = \dfrac{a + b}{ab} \\ \\ \\ \implies \dfrac{ - (a + b)}{(a + b + x)x} = \dfrac{a + b}{ab} \\ \\ \\ \implies \dfrac{ - 1}{(a + b + x)x } = \frac{1}{ab}$


= > - ab = ( a + b + x )x

= > - ab = ax + bx + x²

= > 0 = ax + ab + bx + x²

= > 0 = a( x + b ) + x( b + x )

= > 0 = ( a + x )( x + b )


By Zero Product Rule :

= > a + x = 0 or b + x = 0

= > - a = x or - b = x



Hence,
The value of x is either - a or - b

Answer 2

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20 N

Explanation:

Initially, charges are 6μC and 16μC.

Later on, -8μC is added to both. Then, charges are (6 - 8)μC = -2μC and (16 - 8)μC = 8μC.

q = 6μC, Q = 16μC

q' = -2μC, Q' = 8μC

Force = kqQ/r², let distance be r. Initially:

=> 120 = (9 x 10^9) (6μ*16μ)/r²

=> r² = (9 x 10^9) (96μ²) / 120

=> r² = (864/120) (10^9 x 10^(-6)²)

=> r² = 7.2 x 10^(-3)

When -8μC is added, r is same.Force is:

=> F' = kq'Q'/r²

=> F' = (9 x 10^9) (-2μC*8μC)/(7.2 x 10^(-3))

=> F' = 9 x 10^(9) (-16μ²) / (7.2 x 10^(-3))

=> F' = -(9*6)/7.2 x (10^9 x 10^(-12))/10^(-3)

=> F' = - 20 x 10^0

=> F' = - 20 N

Magnitude of force is 20 N.

Hope this helps you