Question

Ab=100; 1/a-1/b=5; a-b=?​

Answer 1

Решение.

Найти значение выражения  а-b  .

$\bf ab=100\ \ ,\ \ \ \dfrac{1}{a}-\dfrac{1}{b}=5\\\\\\\dfrac{1}{a}-\dfrac{1}{b}=\dfrac{b-a}{ab}=\dfrac{b-a}{100}\ \ \ \Rightarrow \ \ \ \dfrac{b-a}{100}=5\ \ ,\\\\\\b-a=5\cdot 100\ \ ,\ \ b-a=500\ \ \ \Rightarrow \ \ \ a-b=-500$

Answer 2

Let's solve the given equations step by step to find the value of $a - b$.

Given: $ab = 100$ ---(1) $\frac{1}{a} - \frac{1}{b} = 5$ ---(2)

To solve this, let's simplify equation (2) first.

Multiply equation (2) by $ab$ to eliminate the fractions: $b - a = 5ab$ ---(3)

Now, we have two equations: $ab = 100$ ---(1) $b - a = 5ab$ ---(3)

Let's solve these equations simultaneously to find the values of $a$ and $b$.

From equation (1), we can express $b$ in terms of $a$: $b = \frac{100}{a}$ ---(4)

Substitute equation (4) into equation (3): $\frac{100}{a} - a = 5\left(\frac{100}{a}\right)$ $100 - a^2 = 500$ $a^2 = 400$ $a = \pm 20$

Now, substitute the value of $a$ back into equation (4) to find the corresponding value of $b$: If $a = 20$: $b = \frac{100}{20} = 5$

If $a = -20$: $b = \frac{100}{-20} = -5$

Therefore, there are two possible solutions:

1. $a = 20$ and $b = 5$
2. $a = -20$ and $b = -5$

Now, to find $a - b$:

1. For $a = 20$ and $b = 5$: $a - b = 20 - 5 = 15$
2. For $a = -20$ and $b = -5$: $a - b = -20 - (-5) = -20 + 5 = -15$

Hence, $a - b$ can be either 15 or -15, depending on the values of $a$ and $b$.