The least value of expression $x^{2} + 4 y^{2} + 9 z^{2} - 2 x + 8 y + 27 z + 15$ is

15

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- \frac{41}{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $- \frac{41}{4}$
$(x^{2} - 2 x) + 4 (y^{2} + 2 y) + 9 (z^{2} + 3 z) + 15$
${(x - 1)}^{2} + 4 {(y + 1)}^{2} + 9 {(z + \frac{3}{2})}^{2} + 15 - (1 + 4 + 9 \times \frac{9}{4})$
$= {(x - 1)}^{2} + 4 {(y + 1)}^{2} + 9 {(z + \frac{3}{2})}^{2} + 15 - \frac{101}{4}$
$= {(x - 1)}^{2} + 4 {(y + 1)}^{2} + 9 {(z + \frac{3}{2})}^{2} - \frac{41}{4} .$
$∴$ Minimum value is $\frac{- 41}{4}$ .

Suggest Corrections

Similar questions

x^{2} + 4 y^{2} + 3 z^{2} - 2 x - 12 y - 6 z + 14

x^{2} + 4 y^{2} + 3 z^{2} - 2 x - 12 y - 6 z + 14

x^{2} + 4 y^{2} + 8 y - 2 x + 1 = 0

(x + 2 y + 3 z)^{2}

Join BYJU'S Learning Program