Determine |a| and |b| , if (a + b) × (a - b) = 8 and |a| = 8|b| ? - Mathematics MCQ Mathematics Mock Test - 8 2026 | ExamTest.live

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1 mark

Determine ∣ a ∣ and ∣ b ∣, if (a + b) \cdot (a - b) = 8 and ∣ a ∣ = 8∣ b ∣ ?

Solution & Step-by-step Explanation

We are given: (a + b) \cdot (a - b) = 8 ∣ a ∣ = 8∣ b ∣ Expanding the dot product: a \cdot a - a \cdot b + b \cdot a - b \cdot b = 8 Since a \cdot b = b \cdot a, we have: ∣ a ∣^{2} - ∣ b ∣^{2} = 8 Substitute ∣ a ∣ = 8∣ b ∣ : (8∣ b ∣)^{2} - ∣ b ∣^{2} = 8 64∣ b ∣^{2} - ∣ b ∣^{2} = 8 63∣ b ∣^{2} = 8 ∣ b ∣^{2} = \frac{8}{63} ⟹ ∣ b ∣ = \frac{8}{63} = \frac{2 2}{3 7} Now find ∣ a ∣ : ∣ a ∣ = 8∣ b ∣ = 8 \times \frac{2 2}{3 7} = \frac{16 2}{3 7}

Try it yourself before checking the explanation above.

Determine ∣ a ∣ and ∣ b ∣, if (a + b) \cdot (a - b) = 8 and ∣ a ∣ = 8∣ b ∣ ?

\frac{16 2}{3 7}, \frac{2 2}{3 7}

\frac{8 2}{3 7}, \frac{2 2}{3 7}

\frac{16 6}{3 7}, \frac{2 2}{3 7}

\frac{8 3}{3 7}, \frac{2 3}{3 7}

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