Question

I need proper Explanation, I'd.k why but I'm not that clear how to deal with questions like this ~

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Thanks for your effort ~

Answer 1

Hey There!

Let's solve....

`f(x) = ((x + b)(x + c))/((b - a)(c - a)) + ((x + c)(x + a))/((c - b)(a - b)) + ((x + a)(x + b))/((a - c)(b - c)) - 1`

`f( - a) = \frac{( - a + \cancel{b})( \cancel{ - a} + c)}{ (\cancel{b} - a)(c - \cancel{a})} + 0 + 0 - 1 = 1 - = 0`

`f( - b) = 0 + \frac{( \cancel{ - b} + c)( \cancel{ - b} + a)}{ (c - \cancel{b})(a - \cancel{b})} + 0 - 1 = 1 - 1 = 0`

`f( - c) = 0 + 0 + \\ \frac{ (\cancel{ - c} + a)( \cancel{ - c} + b)}{(a - \cancel{c})(b - \cancel{c})} - 1 \\ \\ = 1 - 1 = 0`

`f(x) \to {max}^(m) \: power = 2 \\`

Maximum power where quadratic equation is 2

`\therefore \: f(x) = 0 \\`

x belongs r

Now let's identify

`\to \: ((x + b)(x + c))/((b - a)(c - a)) + ((x + c)(x + a))/((c - b)(a - b)) + ((x + a)(x + b))/((a - c)(b - c)) - 1 = 0`

So x belongs r is identified

Hence finally solved...

I hope it is helpful to you..

cheers!__________