Which of the following expressions CANNOT have a negative value?
a)|a + b| - |a - b|
b)|a + b| - |a|
c)|2a + b| - |a + b|
d)a^2 + b^2 - 2|ab|
e)|a^3 + b^3| - a - b
Is there any another solution apart from putting numbers. It is time consuming in this case.
Quick solution ?
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- prachi18oct
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Since |ab| = |a||b| and a² = |a|², D can be rewritten as a² - 2|ab| + b² = (|a| - |b|)²
Whatever (|a| - |b|) may be, if you square it, you won't create a negative number.
If you don't see that, I find that you can pretty quickly get the answer to this question by plugging in the right numbers.
A) a = -1 b = 4 Plug them in and create a negative number.
B) a = -4 b = 1 Plug them in and create a negative number.
C) a = -1 b = 4 Plug them in and create a negative number.
D) Skip this complicated one for now.
E) Plug in positive fractions and create a negative number.
All the rest can create negative numbers. So D must be the answer.
Whatever (|a| - |b|) may be, if you square it, you won't create a negative number.
If you don't see that, I find that you can pretty quickly get the answer to this question by plugging in the right numbers.
A) a = -1 b = 4 Plug them in and create a negative number.
B) a = -4 b = 1 Plug them in and create a negative number.
C) a = -1 b = 4 Plug them in and create a negative number.
D) Skip this complicated one for now.
E) Plug in positive fractions and create a negative number.
All the rest can create negative numbers. So D must be the answer.
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Perfect Scoring Tutor With Over a Decade of Experience
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Contact me at [email protected] for a free consultation.
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Another approach: look for a way to factor.
D is actually the most factorable one, since a² + b² - 2|ab| is just (|a| - |b|)².
Since no square is negative, we're done ... and much more quickly than if we'd plugged in numbers.
D is actually the most factorable one, since a² + b² - 2|ab| is just (|a| - |b|)².
Since no square is negative, we're done ... and much more quickly than if we'd plugged in numbers.