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Step-by-step explanation:
if 5x - 2y =7 and xy=2
by squaring both the side
(5x-2y)²=7²
(5x)²-20xy+(2y)²=49
(5x)²-20x4+(2y)²=49
(5x)²-40+(2y)²=49
(5x)²+(2y)²=49+40
(5x)²+(2y)²=89________(1)
(5x+2y)²=(5x)²+20xy+(2y)² [by applying the formula]
(5x+2y)²=(5x)²+20x2+(2y)²
(5x+2y)²=(5x)²+(2y)²+40
(5x+2y)²=89+40 [by putting the value from eq (1)]
(5x+2y)²=129
if a+1/a=17/4
(a+1/a)²=a²+(1/a)²+2ax1/a
(a+1/a)²=a²+(1/a)²+2
(17/4)²=a²+(1/a)²+2
(289/16)=a²+(1/a)²+2
289 - 32 = a²+(1/a)²
16
257/16=a²+(1/a)²_______(1)
(a-1/a)²=a²+(1/a)²-2ax1/a
(a-1/a)²=a²+(1/a)²-2
(a-1/a)²=257/16-2
(a-1/a)²=257-32
16
(a-1/a)²=225/16
(a-1/a)=√225/16
(a-1/a)=15/4
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