Question
Download Solution PDFनिर्देश: दिए गए प्रश्न में, दो समीकरण I और II दिए गए हैं। दोनों समीकरणों को हल करें और उपयुक्त उत्तर चिह्नित करें।
I. 12x² + 7x − 12 = 0
II. 8y² − 18y + 9 = 0
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसमीकरण I: 12x² + 7x − 12 = 0
⇒ विविक्तकर = 7² − 4 x 12 x (−12) = 49 + 576 = 625, √625 = 25
⇒ x = [−7 ± 25] ÷ (2 x 12) = [−7 ± 25] ÷ 24
x₁ = (18) ÷ 24 = 3/4 = 0.75
x₂ = (−32) ÷ 24 = −4/3 ≈ −1.333
समीकरण II: 8y² − 18y + 9 = 0
⇒ विविक्तकर = (−18)² − 4 x 8 x 9 = 324 − 288 = 36, √36 = 6
⇒ y = [18 ± 6] ÷ (2 x 8) = [18 ± 6] ÷ 16
y₁ = 24 ÷ 16 = 3/2 = 1.5
y₂ = 12 ÷ 16 = 3/4 = 0.75
मूलों की तुलना:
x₂ = −1.333 < y₂ = 0.75
x₁ = 0.75 = y₂ = 0.75
x₁ = 0.75 < y₁ = 1.5
x₂ = −1.333 < y₁ = 1.5
सभी x-मान, सभी y-मानों से ≤ हैं।
इस प्रकार, सही उत्तर x ≤ y है।
Last updated on Jul 8, 2025
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