If a, b, c, d are in continued proportion, prove that : (i) (ii) (a 2 - b 2 )(c 2 - d 2 ) = (b 2 - c 2 ) 2 (iii) (a + d)(b + c) - (a + c)(b + d) = (b - c) 2 (iv) a : d = triplicate ratio of (a - b) : (b - c) (v)

(i) Since, a, b, c, d are in continued proportion Since, L.H.S. = R.H.S. hence, proved that, . (ii) Since, a, b, c, d are in continued proportion Since, L.H.S. = R.H.S. hence, proved that, (a 2 - b 2 )(c 2 - d 2 ) = (b 2 - c 2 ) 2 . (iii) Since, a, b, c, d are in continued proportion Since, L.H.S = R.H.S, hence proved that, (a + d)(b + c) - (a + c)(b + d) = (b - c) 2 . (iv) Since, a, b, c, d are in continued proportion R.H.S. = triplicate ratio of (a - b) : (b - c) Since, L.H.S. = R.H.S. hence proved that, a : d = triplicate ratio of (a - b) : (b - c). (v) Since, a, b, c, d are in continued proportion Since, L.H.S = R.H.S hence proved that,

Mathematics

If a, b, c, d are in continued proportion, prove that : (i) (ii) (a2 - b2)(c2 - d2) = (b2 - c2)2 (iii) (a + d)(b + c) - (a + c)(b + d) = (b - c)2 (iv) a : d = triplicate ratio of (a - b) : (b - c) (v)

Ratio Proportion

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Mathematics

If a, b, c, d are in continued proportion, prove that : (i) (ii) (a<sup>2</sup> - b<sup>2</sup>)(c<sup>2</sup> - d<sup>2</sup>) = (b<sup>2</sup> - c<sup>2</sup>)<sup>2</sup> (iii) (a + d)(b + c) - (a + c)(b + d) = (b - c)<sup>2</sup> (iv) a : d = triplicate ratio of (a - b) : (b - c) (v)

Ratio Proportion

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