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The non-zero solution of the equation (a – x2) / (bx) – (b – x) /c = (c – x) /b – (b – x2) / (cx), where b ≠ 0, c ≠ 0 is
- a)(b2 + ac) / (b2 + c2)
- b)(b2 – ac) / (b2 – c2)
- c)(b2 – ac) / (b2 + c2)
- d)(b2 + ac) / (b2 – c2)
Correct answer is option 'A'. Can you explain this answer?
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The non-zero solution of the equation (a – x2) / (bx) – (b...
(a – x2) / (bx) – (b – x) /c = (c – x) /b – (b – x2) / (cx)
⇒ (a – x2) / (bx) + (b – x2) / (cx) = (c – x) /b + (b – x) /c
⇒ (a – x2) / (bx) + (b – x2) / (cx) = (c – x) /b + (b – x) /c
Taking LCM of the denominator and combining them into a single factor
[c × (a – x2) + b × (b – x2)] / (bcx) = [c × (c – x) + b × (b – x)] / (bc)
⇒ [ac - cx2 + b2 – bx2] /x = [c2 – cx + b2 – bx]
⇒ b2 + ac – x2 (b + c) = x × [(b2 + c2) – x (b + c)]
⇒ b2 + ac – x2 (b + c) = (b2 + c2) x – x2 (b + c)
⇒ b2 + ac = (b2 + c2) x
∴ x = (b2 + ac) / (b2 + c2)
[c × (a – x2) + b × (b – x2)] / (bcx) = [c × (c – x) + b × (b – x)] / (bc)
⇒ [ac - cx2 + b2 – bx2] /x = [c2 – cx + b2 – bx]
⇒ b2 + ac – x2 (b + c) = x × [(b2 + c2) – x (b + c)]
⇒ b2 + ac – x2 (b + c) = (b2 + c2) x – x2 (b + c)
⇒ b2 + ac = (b2 + c2) x
∴ x = (b2 + ac) / (b2 + c2)
Most Upvoted Answer
The non-zero solution of the equation (a – x2) / (bx) – (b...
(a – x2) / (bx) – (b – x) /c = (c – x) /b – (b – x2) / (cx)
⇒ (a – x2) / (bx) + (b – x2) / (cx) = (c – x) /b + (b – x) /c
⇒ (a – x2) / (bx) + (b – x2) / (cx) = (c – x) /b + (b – x) /c
Taking LCM of the denominator and combining them into a single factor
[c × (a – x2) + b × (b – x2)] / (bcx) = [c × (c – x) + b × (b – x)] / (bc)
⇒ [ac - cx2 + b2 – bx2] /x = [c2 – cx + b2 – bx]
⇒ b2 + ac – x2 (b + c) = x × [(b2 + c2) – x (b + c)]
⇒ b2 + ac – x2 (b + c) = (b2 + c2) x – x2 (b + c)
⇒ b2 + ac = (b2 + c2) x
∴ x = (b2 + ac) / (b2 + c2)
[c × (a – x2) + b × (b – x2)] / (bcx) = [c × (c – x) + b × (b – x)] / (bc)
⇒ [ac - cx2 + b2 – bx2] /x = [c2 – cx + b2 – bx]
⇒ b2 + ac – x2 (b + c) = x × [(b2 + c2) – x (b + c)]
⇒ b2 + ac – x2 (b + c) = (b2 + c2) x – x2 (b + c)
⇒ b2 + ac = (b2 + c2) x
∴ x = (b2 + ac) / (b2 + c2)
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The non-zero solution of the equation (a – x2) / (bx) – (b – x) /c = (c – x) /b – (b – x2) / (cx), where b ≠ 0, c ≠ 0 isa)(b2+ ac) / (b2+ c2)b)(b2– ac) / (b2– c2)c)(b2– ac) / (b2+ c2)d)(b2+ ac) / (b2– c2)Correct answer is option 'A'. Can you explain this answer?
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