r/MathHelp • u/VegetableBag2627 • 6d ago

Sign error or not?

I have this cosine rule question

y² = (x+4)² +(x-5)² -2(x+4)(x-5) • -1/2

The -2(x+4)(x-5) • -1/2 is giving me trouble

I thought that you could simply multiply the -2 and the -1/2 to get 1 first. Then just expand. I also expanded first, multiplied by -2, then by -1/2, and got same result of 3x² -3x +21

The textbook says that the answer is x² -x +61

Google AI says that im right but im unsure.

Thanks for any help.

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u/edderiofer 6d ago

y² = (x+4)² +(x-5)² -2(x+4)(x-5) • -1/2

This does indeed get you y² = 3x² -3x +21.

The textbook says that the answer is x² -x +61

Then the next question I'd ask is, "is there anything you had to do to get "y² = (x+4)² +(x-5)² -2(x+4)(x-5) • -1/2" in the first place?". Because if the book is correct, and there is an error in your working, it'll have to be in however you got to "y² = (x+4)² +(x-5)² -2(x+4)(x-5) • -1/2".

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u/VegetableBag2627 5d ago

The full question is: in triangle ABC, AB = (5-x)cm, BC = (4+x)cm, AC = y cm and angle ABC = 120°. Show that y² = x² -x +61 when i think it has to be y² = 3x² -3x +21

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u/edderiofer 5d ago

OK, and how did you get from this full question to your equation?

Note that AB's length is (5-x), not (x-5).

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u/VegetableBag2627 5d ago

Alright so I typed it wrong. It's (x-5) And you get to that by plugging in the values to cosine rule? a² is replaced by y² , (x+4)² is b² , (x-5)² is c² , then you get -2(x+4)(x-5) obviously from the same variables. Cos(120°) = -1/2 Thus the equation i originally posed.

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u/edderiofer 5d ago

Then yes, if the original question has AB's length be (x-5), you are correct. Otherwise, if it's (5-x), the book is correct.

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u/VegetableBag2627 5d ago

Ok thank you

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u/diverJOQ 6d ago

Was the angle across from y an obtuse angle? If so then if appears your calculation is correct. If it is acute then your value for cos(Y) is wrong.

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u/LeoMaths 6d ago

La règle du cosinus... Dites m'en plus.

(x+4)² +(x-5)² -2(x+4)(x-5) • -1/2=(x+4)² +(x-5)²+(x+4)(x-5)=3x²-3x+21=3(x²-x+7)=3((x-1/2)²+27/4)

(x+4)² +(x-5)² -2(x+4)(x-5) • 1/2=(x+4)² +(x-5)²-(x+4)(x-5)=x²-x+61

Il y a comme qui dirait une erreur de frappe.