Now- as you know the product of roots is 30 - let those roots be a- b- c - R- The minimum value of 10 a -9 b -10 c is

Let us take 3 terms 10a, 9b, 10c We know that AM≥ GM 10a + 9b + 10c/3 ≥ (10 × 9 × 10 × abc)^1/3 10a + 9b + 10c ≥ 3 × (10 × 10 × 9 × 30)^1/3 10a + 9b + 1 ...

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Standard XII

Mathematics

Extrema

Now, as you k...

Question

Now, as you know the product of roots is 30, let those roots be a, b, c $ϵ R$ . The minimum value of 10a + 9b + 10c is __

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Solution

Let us take 3 terms 10a, 9b, 10c

We know that AM $\geq$ GM

$\frac{10 a + 9 b + 10 c}{3}$ $\geq$ ${(10 \times 9 \times 10 \times a b c)}^{\frac{1}{3}}$

10a + 9b + 10c $\geq 3 \times$ ${(10 \times 10 \times 9 \times 30)}^{\frac{1}{3}}$

10a + 9b + 10c $\geq$ 90

So, the minimum value is 90.

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Now, as you know the product of roots is 30, let those roots be a, b, c ϵR. The minimum value of 10a + 9b + 10c is __

Let us take 3 terms 10a, 9b, 10c We know that AM≥ GM 10a+9b+10c3 ≥ (10×9×10×abc)13 10a + 9b + 10c ≥3× (10×10×9×30)13 10a + 9b + 10c ≥ 90 So, the minimum value is 90.

Now, as you know the product of roots is 30, let those roots be a, b, c $ϵ R$ . The minimum value of 10a + 9b + 10c is __

Let us take 3 terms 10a, 9b, 10c

We know that AM $\geq$ GM

$\frac{10 a + 9 b + 10 c}{3}$ $\geq$ ${(10 \times 9 \times 10 \times a b c)}^{\frac{1}{3}}$

10a + 9b + 10c $\geq 3 \times$ ${(10 \times 10 \times 9 \times 30)}^{\frac{1}{3}}$

10a + 9b + 10c $\geq$ 90

So, the minimum value is 90.