If P2 + Q2 + R2 = 82 and Pq + Qr + Pr = 18; Find P + Q + R.

If p² + q² + r² = 82 and pq + qr + pr = 18; find p + q + r.

Sum

(p + q + r)²
= p² + q² + r²+ 2pq + 2qr + 2pr
= 8² + 2(18)
= 64 + 36
= 100
⇒ p + q + r
= `sqrt(100)`
= ± 10.

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Chapter 3: Expansions - Exercise 4.1

Chapter 3 Expansions
Exercise 4.1 | Q 20

What are the possible expressions for the dimensions of the cuboids whose volume is given below?

Evaluate of the following:

(103)³

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104³ + 96³

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Find the following product:

(3x + 2y) (9x² − 6xy + 4y²)

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.

Evaluate: `(3"x"+1/2)(2"x"+1/3)`

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Expand the following:

(3a – 5b – c)²