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प्रश्न
If a, b, c, d are in continued proportion, prove that: (a2 + b2) (c2 + d2) = (b2 + c2)2.
प्रमेय
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उत्तर
a, b, c, d are in continued proportion,
`a/b = b/c = c/d` = k
c = dk, b = ck = dk2, a = bk = dk3
L. H. S.
= (a2 + b2) (c2 + d2)
= [(dk3)2 + (dk2)2] [(dk)2 + d2]
= [d2k6 + d2k4] [d2k2 + d2]
= [d2k4(k2 + 1)] [d2(k2 + 1)]
= d4k4(k2 + 1)2
R.H.S.
= (b2 + c2)2
= (dk2)2 + (dk)2
= d2k4 + d2k2
= d2k2(k2 + 1)2
= (d2)2(k2)2(k2 + 1)2
= d4k4(k2 + 1)2
∴ L.H.S. = R.H.S.
Hence proved.
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क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 7: Ratio and proportion - Exercise 7B [पृष्ठ १२६]
