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Ratio of pairwise sums (a+b):(b+c):(c+a) given: find an expression

This type of question, asked 2 times: CDS 1 2024, CDS 1 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2024

    46
    If (a+b):(b+c):(c+a)=5:7:6(a + b) : (b + c) : (c + a) = 5 : 7 : 6, then what is the value of (a−b+c):(a+b−c)(a - b + c) : (a + b - c) ?

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  2. Question 2

    CDS 1 2025

    44
    If (x+y):(y+z):(z+x)=3:5:6(x + y) : (y + z) : (z + x) = 3 : 5 : 6 and x+y+z=14x + y + z = 14, then what is x2+y2+z2x^2 + y^2 + z^2 equal to ?

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