Algebra> Suppose a,b,c are three distinct real num...

Suppose a,b,c are three distinct real numbers.Let P(x)= (x-b)(x-c) / (a-b)(a-c) + (x-c)(x-a) / (b-c)(b-a) + (x-a)(x-b) / (c-a)(c-b) When simplified P(x) becomes

Nithin , 10 Years ago

Grade 10

2 Answers

Rinkoo Gupta

Last Activity: 10 Years ago

P(x)=(x-b)(x-c)/(a-b)(a-c) + (x-c)(x-a)/(b-c)(b-a) + (x-a)(x-b)/(c-a)(c-b)

=(x-a)(x-b)(x-c)/(a-b)(b-c)(c-a)[(c-b)/(x-a) +(a-c)/(x-b)+(b-a)/(x-c)]

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Rinkoo Gupta

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Sridhar

Last Activity: 8 Years ago

let x=a,

then, substituting in the given equation,

p(x)=1+0+0=1

similarly, p(x where x=b)=1, p(x where x=c)=1

thus, generalized answer can be taken as 1.

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Algebra> Suppose a,b,c are three distinct real num...

Suppose a,b,c are three distinct real numbers.Let P(x)= (x-b)(x-c) / (a-b)(a-c) + (x-c)(x-a) / (b-c)(b-a) + (x-a)(x-b) / (c-a)(c-b) When simplified P(x) becomes

Nithin , 10 Years ago

Rinkoo Gupta

Sridhar

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