Question

35. If a and b are numbers when does lal=|b|? Give examples.

Answer 1

For the given absolute value equations:

• |a| = |b|  Is true only if a = ± b
• |-c| = |d| is only true if c = ± d

When the absolute values of two numbers are equal?

We define the absolute value function as:

• |x| = x if x ≥ 0.
• |x| = -x if x < 0.

Then, if a and b are numbers (I assume that it refers to real numbers) then the equation:

|a| = |b|

if a > 0, b > 0, then:

a = b

if a > 0, b < 0, then:

a = -b

if a < 0, b > 0.

-a = b

if a < 0, b < 0

-a = -b

With these 4 relations we can conclude that |a| = |b|  Is true only if a = ± b

We similarly have the other equation:

|-c| = |d|

Also for real numbers, this is exactly the same as the case above, that equation is true only when:

c = ± d

If you want to learn more about absolute value functions:

brainly.com/question/3381225

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