in a quadrilateral four sides are a,b,c,d.if a2+b2+c2+d2= ab+bc+cd+ad=26 cm,then b+c=?
Answers
b+c = √26 , if in a quadrilateral four sides are a,b,c,d a² + b² + c² + d² = ab + bc + cd + ad = 26
Step-by-step explanation:
a² + b² + c² + d² = ab + bc + cd + ad = 26
Multiplying by 2 both sides
=> 2a² + 2b² + 2c² + 2d² = 2ab + 2bc + 2cd + 2ad = 52
2a² + 2b² + 2c² + 2d² = 52
=> a² + b² + b² + c² + c² + d² + d² + a² = 52
=> (a - b)² + 2ab + (b - c)² + 2bc + (c - d)² + 2cd + (d - a)² + 2ad = 52
=> (a - b)²+ (b - c)² + (c - d)² + (d - a)² + 2ab + 2bc + + 2cd + 2ad = 52
=> (a - b)²+ (b - c)² + (c - d)² + (d - a)² + 52 = 52
=> (a - b)²+ (b - c)² + (c - d)² + (d - a)² = 0
=> a = b , b = c , c = d , d = a
=> a = b = c = d
a² + b² + c² + d² = 26
=>4b² = 26
=> b² = 13/2
=> b = √13/2
b + c = √13/2 + √13/2
= 2√13/2
= √26
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