Pertanyaan

Jika a + b + c = 0, maka nilai dari b 2 + c 2 − a 2 1 + c 2 + a 2 − b 2 1 + a 2 + b 2 − c 2 1 = ...

Jika a + b + c = 0, maka nilai dari $\frac{1}{b ^{2} + c ^{2} - a ^{2}} + \frac{1}{c ^{2} + a ^{2} - b ^{2}} + \frac{1}{a ^{2} + b ^{2} - c ^{2}} = ...$

0
$fraction numerator 1 over denominator a plus b end fraction$
$fraction numerator 1 over denominator a minus b end fraction$
$fraction numerator a plus b over denominator a minus b end fraction$

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Diketahui a + b + c = 0 maka c = - (a + b) sehingga:

Diketahui a + b + c = 0

maka c = - (a + b)

sehingga:

$fraction numerator 1 over denominator b squared plus c squared minus a squared end fraction plus fraction numerator 1 over denominator c squared plus a squared minus b squared end fraction plus fraction numerator 1 over denominator a squared plus b squared minus c squared end fraction equals fraction numerator 1 over denominator b squared plus open parentheses negative open parentheses a plus b close parentheses close parentheses squared minus a squared end fraction plus fraction numerator 1 over denominator open parentheses negative open parentheses a plus b close parentheses close parentheses squared plus a squared minus b squared end fraction plus fraction numerator 1 over denominator a squared plus b squared minus open parentheses negative open parentheses a plus b close parentheses close parentheses squared end fraction equals fraction numerator 1 over denominator b squared plus a squared plus 2 a b plus b squared minus a squared end fraction plus fraction numerator 1 over denominator a squared plus 2 a b plus b squared plus a squared minus b squared end fraction plus fraction numerator 1 over denominator a squared plus b squared minus open parentheses a squared plus 2 a b plus b squared close parentheses end fraction equals fraction numerator 1 over denominator 2 b squared plus 2 a b end fraction plus fraction numerator 1 over denominator 2 a squared plus 2 a b end fraction plus fraction numerator 1 over denominator negative 2 a b end fraction equals fraction numerator 1 over denominator 2 b open parentheses b plus a close parentheses end fraction plus fraction numerator 1 over denominator 2 a left parenthesis a plus b right parenthesis end fraction minus fraction numerator 1 over denominator 2 a b end fraction equals fraction numerator 1 over denominator 2 open parentheses a plus b close parentheses end fraction open parentheses 1 over b plus 1 over a close parentheses minus fraction numerator 1 over denominator 2 a b end fraction equals fraction numerator 1 over denominator 2 open parentheses a plus b close parentheses end fraction open parentheses fraction numerator a plus b over denominator a b end fraction close parentheses minus fraction numerator 1 over denominator 2 a b end fraction equals fraction numerator 1 over denominator 2 a b end fraction minus fraction numerator 1 over denominator 2 a b end fraction equals 0$